Almost all continuities share at least one thing in common: a Cybertron wracked with civil war.
The demigod Primus created the Transformers with the intention that they would all be righteous and obedient. However, his creations quickly became divided between the Autobots and Decepticons. (Grimlock once theorized that this was some kind of natural yin-yang balance.) According to the Liege Maximo, "When the first named Prime was created, so was the Liege Maximo. Moreover, from the Liege Maximo came the Decepticons and all their subsequent generations. Evil... is infinite!"
According to Optimus Prime, as the original Transformers reproduced through a process similar to cell division, Primus's goodness became more and more diffuse in succeeding generations, and Transformers were arising who had none of "the essential purity of our creator's vision." A genetic fail-safe eventually kicked in, causing them to forget how to reproduce without the aid of the Creation Matrix. However, the moral dilution had already gone too far.
The inevitable result was a planetary civil war, begun by Megatron, who sought to convert the planet into a "cosmic dreadnought." His goal was never realized, but the cataclysmic forces that the war unleashed pushed Cybertron out of its orbit around Alpha Centauri. As the planet careened through space, it was pulled toward Sol and a turning point in the war. The Main Asteroid Belt between Jupiter and Mars was in Cybertron's path, so Optimus Prime and an Autobot team abandoned the war briefly to launch the Ark and clear a path for their home world. They succeeded, but Megatron took advantage and attacked them immediately afterwards. That battle ended with the combatants crashing on prehistoric Earth and lying catatonic for four million years.
Nevertheless, even with their great leaders gone, the Transformers on Cybertron continued their war. In the absence of the Creation Matrix (which was in Prime's chest), the Decepticons eventually rediscovered the lost method of "budding" reproduction. The resulting new Transformers were very powerful and completely devoid of morality. With each new Transformer created, there also appeared a strange by-product: a dark, cloudy mass that coalesced with other such masses and floated off into space, apparently harmless for the moment.
Meanwhile, the "second-generation" Decepticons laid waste to the Autobot forces, but they were dissatisfied with the wasteland that Cybertron had become, so they left in search of new challenges. Many of the older Decepticons (perhaps all of them) remained on Cybertron and maintained control for millions of years.
On Earth, the damaged Ark lay untouched beneath a volcano for four million years, but in 1984, a volcanic eruption jogged its systems and caused its computer to reactivate. The ship repaired its passengers, Autobot and Decepticon alike, and thus the war spread on Earth. Megatron established contact with Cybertron, and Lord Straxus, governor of the province of Polyhex, organized the construction of the first space bridge. Megatron planned to use it to ship energy from the resource-laden Earth to the barren Cybertron, but his plans never fully succeeded.
At this time, the Cybertronian Autobots were mainly fighting in underground resistance movements. Their command centres were secret Autobases hidden in Decepticon territory. Optimus Prime and his companions were regarded as heroes (perhaps legends) by the freedom fighters, and news of their survival was welcomed joyously. However, global communication must have been inefficient, for that encouraging news never reached some 'Bots, such as Fortress Maximus and his small army. If Fort Max had heard about it, perhaps he never would have reached the despair that led him to leave Cybertron. Perhaps he and his companions never would have journeyed to the peaceful planet Nebulos, where they hoped to avoid the Transformers war. Then Scorponok and his minions wouldn't have followed them, and the disease of war would have passed over that world.
However, that's not what happened. The Cybertronian Civil War did spread to Nebulos, and some of the humanoid residents joined the conflict by binary bonding to Transformer hosts, becoming the Headmasters and Targetmasters. The Transformers would eventually leave the planet (and its inhabitants poisoned their own fuel supply to keep them away). Nevertheless, the technology of binary-bondage would stay with the Transformers and become a new facet in the ongoing wars.
Throughout this time, the war's two main battlegrounds remained Cybertron and Earth. Leadership squabbles were common, especially since neither side seemed to have a central command governing the armies on both planets. Developments on one front sometimes came as a surprise to the other. For instance, Prime seemed taken aback when he met the first two Autobot Micromaster patrols on Earth, and they had to explain the new Cybertronian trend of downsizing to conserve energy.
However, the next major development in the war would do away with much disunity. The accidental waking of Primus alerted Unicron to Cybertron's location. Prime knew that the Matrix could defeat the chaos-bringer, so he sent teams looking for his own old corpse, which still bore it. However, they were beaten to the punch by the Decepticon Lord Thunderwing, who merged with the Matrix as the Primes had. Thunderwing turned it to evil and attacked the Autobots on board the space borne Ark. He was defeated and sent tumbling through space, but Prime made no effort to recover the Matrix again.
Rather, he sought to prepare for Unicron's coming by trying to unite all Cybertronians. He surrendered to Scorponok on Earth in an effort to begin peace talks. One minor Decepticon civil war later, the combatants were all ready to lay down their arms. Then, suddenly, almost every Earthbound Transformer was transported by Primus to Cybertron. There they fought Unicron in a battle that destroyed Primus himself (along with Scorponok and many others). Thunderwing and the tainted Matrix reappeared, but even it couldn't defeat Unicron. However, when Optimus touched the Matrix, its evil was purged, and the full force of Primus's life essence was unleashed. The result was the destruction of both Unicron and the Matrix (and Optimus, in the explosion).
For a short time, all Cybertronians were united, but Cybertron began to show signs of massive global deterioration. In the absence of Primus, it was theorized, the planet was falling apart. Their true natures showing through, the Decepticons sabotaged the Autobots' spacecraft and, under Bludgeon's command, sought out other worlds to conquer. Grimlock found replacement ships and led the Autobots in pursuit. Meanwhile, on Cybertron, Hi-Q (Optimus's Powermaster partner) and the Neo-Knights) found the Last Autobot, a guardian whom Primus had created to control the changes that Cybertron would undergo in his absence. Not only did the Last Autobot successfully guide Cybertron's re-creation, but he also re-made Hi-Q into a new version of Optimus Prime. Then they all went to the planet Klo, where Bludgeon's forces were slaughtering Grimlock's troops. The Last Autobot began resurrecting the dead Autobots, and the renewed armada was able to defeat the Decepticons. Bludgeon swore to exile his army in shame.
The Autobots returned to the re-created Cybertron (although it's not known how the planet was changed), and peace existed for few years. However, Bludgeon was bolstering his forces by attacking far-off civilizations and stealing their technology. He also constructed an army of new Decepticons, but he needed the Matrix to bring them to life. For some reason, Prime still had the Matrix, so Bludgeon used his giant starship, the Warworld, to decimate Earth. He knew that Prime would return and defend the planet, so all he had to do was wait. During that waiting period, though, Megatron returned and destroyed Bludgeon, reassuming command.
Prime, meanwhile, was occupied with other concerns. The second-generation Decepticons had returned from deep space, where they had been re-making planets in Cybertron's image. They considered the older Cybertronians inferior and small-minded, insects who could either join them or suffer the same fate as any other life forms. Jhiaxus, their Liege Centuro (sort of a field commander), became obsessed with hunting Prime down. Thus, when Prime learned about Bludgeon's attacks on Earth, he saw it as an opportunity to warn the Decepticons about the threat Jhiaxus posed to all Cybertronians.
But Megatron rebuffed him and tried to take on Jhiaxus himself. The attempt failed, and Megatron returned to Prime, accepting the truce. Jhiaxus also came to Earth and attacked them. In the midst of the battle, suddenly there appeared the Swarm, that nebulous by-product of the second-generation Decepticons' creation. It had been wandering the galaxy, searching for the Transformers, and destroying metal as it went along. When it got to Earth, it began feasting on all Transformers, new and old, and the entire race nearly fell. Even Jhiaxus was destroyed. However, Prime was able to reclaim the Matrix, and when the Swarm devoured him, the power of the Matrix flowed through it. It was transformed into a force of life, with a new purpose (although it's not known what that purpose was). Prime was re-created, and he remained the leader of the Autobot-Decepticon alliance. Meanwhile, in a sector of space known as the "outer fringes," in a strange complex called the Hub, the Liege Maximo, supreme leader of the Decepticons, showed little grief over Jhiaxus's defeat. He also expressed his confidence in his forces, claiming that the day of reckoning would yet come for Prime and his "ridiculous" alliance.
G1 cartoon continuity
It is unknown if there were any planetary civil wars among the Quintessons while they controlled Cybertron (although there was certainly crime and punishment). The first known war was the robot slave revolt around 11 million years BCE. The Quintessons had built Cybertron as a factory to produce two types of slave robots: military hardware and consumer goods. For a million years, the Quintessons maintained control, but when the robots began to develop emotions, they turned on their cruel Quintesson masters.
The first revolt was carried out by, interestingly enough, a band of non-warrior robots (workers, scientists, and technicians). A slave called A3, who somehow possessed a secret weapon called a Coda Remote, led them. However, Quintessons from the year 2006 used a time machine to kidnap A3 the night before the final assault. Just as that occurred though the future a team of Autobots attacked Quintesssons. The Autobots found themselves outnumbered and outclassed, so, in desperation, they jumped through the "time window" and into the past. They were rescued from the attacks of a Quintesson Dark Guardian robot by Beta, the acting leader of the revolutionaries, and accepted into the fold because they too wore the "slave brand" (the Autobot symbol). Beta decided to lead the attack on Hive City (which the Quintesssons had built with slave labour) with or without A3, and the Autobots simply followed along. The attack went well at first, but the motley band of freedom fighters soon proved to be no match for the Quintessons' many Dark Guardians. Suddenly, however, A3 returned from the future and used his Coda Remote, which was activated when he removed his slave brand and turned its reverse side to the Dark Guardians. It emitted a wide beam of light that caused the giant robots to stop in their tracks and fall down. A3 urged the Autobots to return to the future, which they did, and the Quintesson time machine was destroyed upon their arrival.
After the slaves drove the Quintessons away from Cybertron, peace reigned. However, the division between consumer goods and military-hardware was becoming acute, as the two groups had even named themselves differently: the consumer goods robots called themselves Autobots, and the military-hardware robots were known as Decepticons. While the Autobots preferred a peaceful existence, the Decepticons wanted conquest. For a time, the Decepticons succeeded.
(It should be noted that the Matrix was already in existence, apparently being passed from one Autobot leader to the next, as is the practice today.)
The Autobots couldn't match the brute strength of the Decepticons, so they turned to stealth, learning the art of transformation. Using this new technology, they defeated the Decepticons and ruled for many centuries in a "Golden Age." Peace was kept with the use of Guardian robots (presumably based upon the Quintessons' Dark Guardians), sentinels that protected cities, quelled uprisings, and generally did the dirty work of war. However, the Decepticons eventually learned to transform and also developed some form of anti-gravity that allowed them to fly without the use of jets. They also built a powerful leader for themselves: Megatron.
Thus, circa 9 million years BCE, the war began anew. Megatron led his army from victory to victory, targeting mainly power centres to fuel his troops and build his forces. While the Guardian robots were powerful enough to strike fear in the Decepticons, even those giants were suffering at Megatron's hands. Even the safety of the Matrix was in question, so Alpha Trion (formerly known as A-3) kept it in hiding for many years. It was to this time of violent flux that the newly created Aerialbots were accidentally sent from the year 1986.
They soon met a young, energetic worker at an energy-shipment facility. This robot, Orion Pax, was in awe of the Decepticons, but his feelings changed when Megatron attacked his workplace and gravely wounded him, his girlfriend Ariel, and his friend Dion. The Aerialbots took Orion to Alpha Trion, who was devising new ways to combat the Decepticons. Alpha Trion rebuilt Orion into Optimus Prime, the first of a "new breed" capable of fighting Megatron. He also rebuilt Ariel into Elita One, but it is unknown if Dion got similar treatment.
At some point, Prime was named leader of the Autobots, and Alpha Trion gave him the Matrix. (This may have been when he was first created; the timeline is uncertain. There's even confusion about when Alpha Trion acquired the Matrix in the first place; when he is seen taking it, he looks older than he did when he built Prime.) For the next five million years, the war raged on, draining Cybertron of its resources. Even the buildings and landscapes, which used to glow with radiant energy, became dull and barren. In search of new energy sources, Optimus Prime led a team of Autobots on an interplanetary expedition that ended when Megatron attacked and boarded their ship. As the Autobots and Decepticons fought, the ship strayed too close to the nearby planet Earth and the resulting crash and rendered them catatonic.
For the next four million years, Shockwave commanded the Decepticons on Cybertron, who maintained the upper hand. When the Earth-bound Transformers were revived during the Cold War in 1984, Megatron schemed to harness Earth's resources and send the energy to Cybertron. With the invention of the spacebridge, interplanetary travel became very easy, and Megatron's plans came closer to fruition. He may have succeeded, at least in part, for by the year 2005 the Decepticons had driven the Autobots off of Cybertron and were poised to attack Autobot City on Earth. When they did attack, the Autobots were able to fend them off, but not without losing Optimus Prime. Megatron had also been mortally wounded, but Unicron, who re-created him, revived him into the ultra-powerful Galvatron. Under Galvatron's command, the Decepticons hunted down the Earth-based Autobots while Unicron devoured the two Autobot-controlled Cybertronian moons. Unicron then began to attack Cybertron and the Decepticons, doing severe damage, until the young Autobot Hot Rod activated the Matrix of Leadership and, turning into Rodimus Prime, destroyed Unicron.
Having been decimated at Unicron's hands, the Decepticons retreated to the burned-out world called Chaar. Rodimus Prime announced this to be the end of the Cybertronian wars, but he was clearly overconfident. When Galvatron returned and reunited the tattered Decepticon army, the war began raging again. This time, a new wrinkle was added in the form of the Quintessons, who formed tenuous alliances with the Decepticons in an attempt to reclaim Cybertron. In addition, two groups of 'Bots and 'Cons stumbled upon Nebulos, where they allied with the humanoid inhabitants by binary-bonding. Itself a milestone in the war, this also led to another turning point: the institution of a new Golden Age. The Autobot-allied Nebulans helped reverse one of Galvatron's schemes, and the result was sucking energy out of the sun and into the material of Cybertron itself. Thus, the planet once again glowed with golden energy, still under exclusively Autobot rule, while the Decepticons remained elsewhere.
A note about nomenclature: The current conflict (i.e., the one that's been going on for nine million years) has been called both the "Third Cybertronian War" and the "Great War." The Second Cybertronian War, then, was probably the original Autobot-Decepticon battle that began after the Quintessons were driven away, and the First Cybertronian War would be that slave revolt. This nomenclature however, was never visibly demonstrated until after the Transformers became fully aware of their origins as creations of the Quintessons. It is apparent that a different numerical identification system for the conflicts was in use beforehand; given statements by Perceptor, who referred to the third war as if it had occurred quite some time ago. Sandstorm, noted that his ancestors left Cybertron after “the Fourth Great War.”
Note Other than the fact that the first Post-Unicronian conflict took place in the year 2010 instead of 2006, the war in the Japanese version of events are largely the same; the continuities split during the Headmaster period.
Dreamwave Generation One comics
Dreamwave Transformers/G.I. Joe comics
Devil's Due G.I. Joe vs. The Transformers comics
IDW Generation One comics
In this continuity, the opening skirmishes of the Great War broke out during economic and civil unrest due to greed from senators such as Decimus and Ratbat. A former asteroid miner rose to glory in the gladiatorial pit known as the Forge and made a name as Megatron. With financial and material aid from Ratbat via Soundwave, he gathered an army of malcontents and began a series of daring raids upon the establishment. With the death of Sentinel Prime, Megatron had secured his reputation as a warlord to be feared.
As the war spread across Cybertron, Decepticon scientist Thunderwing saw the devastation it was visiting upon the planet and warned his peers that the Cybertronian race would need to adapt. Roundly dismissed by them and even by his commander Megatron, he became desperate. Testing his newly invented Pretender process on himself, he accomplished what he had set out to do, but at the cost of his sanity. Spurred on by forces he could not comprehend, he became the avatar of the planet's destruction, wreaking havoc upon Autobot and Decepticon alike. Though he was eventually defeated, Cybertron had to be abandoned, its environment unliveable. The mad genius was given a dubious honour as Thunderhead Pass was named for him.
As the war spread beyond their home planet, the Cybertronians at some point reached an agreement in the Code of Interplanetary Conflict. This accord limited the ability to wage war openly upon non-aligned planets, and had strict provisions against Cybertronian technology being sold on the open market.
Recently, the discovery of the Energon derivative known as Ore-13, seeded on an insignificant backwater world by the AWOL Decepticon genius Shockwave, threatened the status quo of the conflict. Realizing its potential, even Megatron feels tempted to discard the careful planning that allowed the Decepticons to take many worlds. With this prize within his grasp, the warlord calls in Decepticon weapon of mass destruction Sixshot.
In 2007 (or so), the Autobots would lose the Great Wars for good to the Decepticons. Betrayed by one of their own, the Autobots ended up being slaughtered on a galaxy-wide scale. Optimus Prime himself critically damaged as his men holed up back on Cybertron. Megatron, most of his Earth infiltration team, and a few joiners went to Earth to establish control." 
IDW Evolutions comics
Continuity note: The Beast Wars writers loosely based their history on the G1 animated series and Marvel comics. However, they stated that those original G1 stories had the same truth-value as Arthurian legend.
In the Beast era, there are few direct sources for Cybertronian history. No occurrences of time-travel to ancient Cybertron are known, and there seem to be no incidents of access to knowledge bases like the Matrix of Leadership. In fact, the Maximal Elders show evidence of having kept a tight lid on historical information. Therefore, what we do know is in scraps:
Cybertron was once gripped by a war between the Autobots and the Decepticons known as the Great War. One key event was the familiar crash-landing of the Ark on prehistoric Earth, bearing Optimus Prime, Megatron, and many of their classic followers. After awakening, Megatron would encode a message to Cybertron on the Voyager Golden Record (also known as the Golden Disk.). It's also known that Unicron had some presence during the war. (The Vok assumed Unicron's form based on a mind-scan of Optimus Primal for an "authority figure." Also, when Starscream's ghost made an appearance, he claimed to have been destroyed by Unicron, to cover for his actual demise at Galvatron's hands.)
The war concluded with a peace agreement of some sort called the Pax Cybertronia. This appears to have marked the end of 'Bot and 'Con dominance over the planet, in favour of their descendants, the Maximals and Predacons. If either side actually won, it must've been the Autobots and Maximal’s, since the Predacons quietly chafed under the political peace. In addition, several Decepticons (such as Ravage) had been granted amnesty, which seems to imply that the others were criminals.
It was a rogue Predacon calling himself Megatron who finally decided to do something about the Predacons' situation, 300 years after the end of the Great War. He stole the Golden Disk and obeyed his namesake's orders contained therein, time travelling back to prehistoric Earth. Ostensibly, he was simply going to harvest the planet's energon, but he eventually decided to follow though with the original Megatron's orders: He broke into the Ark and tried to destroy Optimus Prime. This created a time storm that nearly changed the history of the war, but the Maximal’s were able to undo his damage.
While the Maximal’s were taking Megatron back to their future Cybertron, Megatron escaped and slipped out of the time stream early. This gave him time to reach Cybertron and release a virus that paralyzed all the Transformers before the Maximals arrived. He extracted his victims' sparks and rebuilt their bodies into an army of Vehicons that swept over the planet. When the Maximals did arrive, they found themselves running for their lives on a nearly dead world.
Their battles eventually resulted in the destruction of both Megatron and Primal, plus the transformation of Cybertron into a technorganic planet. Megatron's victims all returned in new bodies, and it's unclear how much of the old Maximal/Predacon division remained.
IDW Beast Wars comics
Robots In Disguise
Very little is known about how this war began. We know Ultra Magnus and Optimus Prime both fought in it, with Magnus distinguishing himself. Who the enemy was is unconfirmed, though it would presumably be the Predacons. It appears the conflict had ended on Cybertron by the time Vector Sigma was choosing a new Autobot Commander-in-Chief. (Ultra Magnus and Optimus both refer to the Civil Wars being in the past tense at this time.)
However, the Predacon Council were still plotting conquest, and Megatron's forces began a campaign of attacking and destroying alien worlds for their energy. Optimus Prime was chosen to lead an army against them. This would eventually reach Earth, when the Council sent Megatron there to find Fortress Maximus and the tyrant kidnapped a prominent scientist Doctor Kenneth Onishi. Prime and his Autobots were already in wait, having established a base, Earth disguises, and a Global Space Bridge network.
Armada, Energon and Cybertron cartoon continuity
Armada & Energon comics
For generations, the inhabitants of Cybertron lived in peace, under the joint leadership of the brothers Optimus Prime and Lord High Protector Megatron. While Megatron was firm, Prime was fair, and the two personalities created a balance. That changed, however, when Megatron sought the All Spark, which gave life to all Transformers. He raised an army, the Decepticons, who sought the All Spark to give them the power to conquer other worlds. To counter Megatron, Prime raised his own army, the Autobots. Although the Autobots fought bravely, the Decepticons were the more ferocious warriors, and Megatron began to gain ground. In a desperate move, Prime sent the All Spark into deep space, and Megatron pursued it. Both crashed on Earth, and disappeared for many years. The war became a search for the All Spark, with the Decepticons, led by Starscream, searching for both the All Spark and Megatron.
Few details are known of the Great War in this continuity, only which it raged for millions of stellar cycles. Ended with Megatron and his Decepticons being driven from Cybertron by the Autobots, led by Ultra Magnus; that the Autobots’ access to the AllSpark and space bridges were apparently integral to their victory.