Note: Exodus tells it's own account of Jazz's backstory, and of the Autobots evacuation from Cybertron, which conflicts with the Cybertron games.
Jazz was a cultural investigator who came to the Hall of Records to analyze new data from the Communication Grid, which was where he befriended Orion Pax. He secretly attended the gladiatorial combat in Iacon. When Orion told him about the gladiator Megatronus and his movement to abolish the caste system, Jazz suggested going to Kaon or at least contact him, considering how much Orion agreed with his ideas. Orion followed his advice, and contacted Megatron. Orion practiced self defense with Jazz following a suggestion in his and Megatron's brainstorms. Jazz was suspicious of Megatron though, and warned Orion that he was the sort of bot that would kill him if he felt he betrayed his ideas.
After terrorists committed acts of violence in Megatron's name, Megatron took Orion to a gladiatorial pit in Iacon, exposing Jazz's secret. Jazz attended the High Council's hearing with Orion and Megatron and gestured to Orion to be strong in the face of the Council's accusations. After Orion was promoted to Optimus Prime, Jazz joined his Autobots and told him not to mourn every lost soldier following the capture of Fort Scyk. He, Optimus and Sideswipe led the Autobots to victory at Kalis by taking down the combiner Bruticus Maximus.
Jazz was with others in Optimus' inner circle—Bumblebee, Ironhide and Prowl—when the war turned into a siege of Iacon and Alpha Trion informed Optimus of a new weapon aboard Trypticon Station. He asked them what they knew about energon. Jazz joked that it was time for school, but Prowl chided him for making fun at Alpha Trion's expense and that if the Archivist had something to say, it was important. Alpha Trion explained Energon was the emanation of Primus, to which Jazz quipped he still didn't know what that was, prompting laughter from Ironhide and Prowl. Alpha Trion then said Megatron's weapon was Dark Energon, the essence of Unicron, and Jazz stopped joking when he realized a confrontation with superpowered Decepticons was imminent.
Indeed, it was Jazz's team that first encountered Darkened Decepticons at Maintenance Port A46, along the Iacon-Kalis energy conduit. Though faster than any Decepticon and able to evade them, the Darkened gladiators wiped out his six-member unit. Autobots continually had to flee whenever Darkened Decepticons appeared, but Optimus realized Dark Energon was inefficient and Decepticons always had to retreat if a battle was prolonged. Jazz suggested they continue to fight back.
When Megatron came to Iacon to steal the Plasma Energy Chamber, Jazz fought with Omega Supreme against the Darkened Decepticons, but Megatron was too powerful and took the Chamber to contaminate the core of Cybertron. Jazz went with Optimus and Prowl in rescuing Sentinel Prime from Kaon, getting briefly paralyzed by a guard's whip, though he was still able to hear Sentinel's last words. After Sentinel's funeral in Iacon, Optimus asked Jazz if he believed the Thirteen original Transformers existed, to which he replied he didn't, though he saw great metaphorical value in them.
Optimus journeyed to the core, purifying it and obtaining the Matrix of Leadership. He returned ordering the commencement of Project Generation One and the evacuation of Cybertron, a notion Jetfire found suicidal but which Jazz defended. He coined the ship's name: the Ark. Jazz helped down Trypticon as part of the Eight Track crew—bearing the brunt of Trypticon's drones' attacks with Prowl and Ironhide—before boarding the Ark. Despite Jazz's fears about the last space bridge, it transported the Autobots to a spiral galaxy away from the Decepticons and near the AllSpark.
War for Cybertron
Jazz was one of many Autobots who was captured by the Decepticons and sent to the Kaon prison complex. He passed the time in incarceration by doing push ups in his cell, waiting for the day he would be able to break out. That chance came when Optimus, Bumblebee and Sideswipe (who had allowed themselves to be captured) opened all the cells in Kaon during a attempted rescue mission of Zeta Prime. Air Raid led the prisoners to transport ships, with which they escaped. He could be seen waving Autobots onto the closest ship through the window from above.
Jazz was among the Autobot captives in Kaon Stadium when a team of escaping Autobots teamed up with him to escape. Jazz had figured a way out of the Stadium, but first the Autobots had to fight him to buy them some time. After the fight and Jazz's defeat, Jazz left with the Autobots free at last.
Rise of the Dark Spark
Jazz led the Autobot attack on Kaon to reclaim the Dark Spark from the Decepticons. When Bruticus incapacitated and captured Cliffjumper, Jazz called for a ceasefire and begged Shockwave to return Cliffjumper, claiming that the Decepticons had already got what they wanted. Shockwave responded by simply laughing as he led Bruticus and unconscious Cliffjumper into Kaon.
Jazz reported Cliffjumper's capture to Optimus, and subsequently accompanied his leader to the Decepticon base Kolkular to retrieve their comrade and destroy the Dark Spark. Jazz was responsible for freeing Cliffjumper while Optimus covered them, but was captured, along with Optimus and Cliffjumper, by Megatron. They were freed when Jetfire commandeered the wrecked Trypticon's weapons systems and fired upon Kolkular, and the 'bots parted ways when Optimus ordered Jazz to take Cliffjumper and escape the base while Prime faced Megatron himself in order to reclaim the Dark Spark.
Fall of Cybertron
After Grimlock went missing from his post, Optimus Prime met Cliffjumper and Jazz in the armory as they were preparing to go find Grimlock and his team. Sideswipe took the duo in a dropship to the Sea of Rust where they explored the ruins, with Cliff managing to save Jazz's life when he was trapped under debris. The pair tracked a distress signal to a huge pit, which Jazz opted to venture into alone. He managed to find Sludge, albeit non-functional, and immediately got into trouble in the form of Insecticons. He escaped by flooding the pit with toxic waste. Exploring further, they found an energon lake and spotted the huge tower in which Shockwave was conducting his space bridge experiments. Jazz and Cliffjumper infiltrated the facility, eventually finding Shockwave himself. The Decepticon trapped Cliff behind a forcefield and Jazz was forced to fight off wave after wave of Insecticons while the other Autobot worked out a way to destroy the base. They escaped just before the place exploded and reported the energon lake back to Optimus before returning to finish preparing the Ark for launch.
After takeoff, the Ark headed for a space bridge Shockwave had opened, but was pursued by the Decepticons aboard their flagship the Nemesis. They attacked the Ark and Jazz responded to a report that Bruticus was on board. His arrival was cheered on by the defending Autobots, but even though Jazz made full use of his grapple and shot Bruticus repeatedly in the face the giant Decepticon seemed unstoppable. However, with the help of air strikes from Jetfire and the Aerialbots, Jazz managed to knock Bruticus off-balance enough for the air strikes to knock him clean off the Ark and spiral away into space.
After passing through the unstable Space Bridge, Jazz and the Autobots aboard the Ark found themselves in the vicinity of a Cybertronian colony world called Velocitron. They located it in part thanks to a mysterious starmap projected outwards from Optimus Prime's chest by the Matrix itself. Jazz was part of Optimus Prime's initial landing team, who made contact with the planet's rulers, Override and Ransack. It was a time of great stress between Velocitron's rulers, and the Autobots' arrival from mythical Cybertron only exacerbated the situation. Worse still, active acts of sabotage led the Autobots to the conclusion that one of their crew was actually a Decepticon agent. Jazz and Prowl conferred with Optimus about the situation, but ultimately concluded there was little they could do at the moment other than remain on guard. Although the Autobots secured an ally in Override, they left Velocitron on the brink of civil war during their departure, as Ransack's followers had been corrupted by the Decepticon rhetoric of "peace through tyranny" spread by the Ark's traitor.
The next leg of their journey through the Space Bridge brought the Autobots to fabled Junkion, a world composed entirely of space junk. Jazz mouthed off about the poor conditions of the planet and the somewhat meandering nature of their "quest", forcing Optimus Prime to put his foot down about his old friend's lack of discipline. Jazz remained behind on the Ark during the initial visit to Junkion. Of course, this meant he was on hand when the ship exploded and crashed down to Junkion's surface thanks to another round of sabotage. The Autobots went to work repairing the Ark, with the relative assistance of the Junkions. Prowl's investigations into their traitor turned up an astonishing culprit—Makeshift, one of the fabled "Shifters" descendant from Amalgamous Prime, with the ability to change appearances at will. Jazz and Optimus managed to identify and trap the Shifter in a stasis field, ending his threat to the Autobots.
The Decepticons eventually arrived on Junkion in force, and the two sides warred over a hidden treasure at the planet's core, the Requiem Blaster. A weapon capable of drawing infinite power from nearby stellar sources, the Requiem Blaster had its own gravity field, and had literally been the core around which Junkion's "junk" had formed. The fighting over the Requiem Blaster ripped the planet apart, but both sides eventually called off the melee and abandoned the Blaster after learning the location of the Allspark itself. Optimus Prime, Jazz, and the rest of the Autobots boarded the Ark and began the long race to reach their civilization's greatest prize before Megatron could.
Robots in Disguise
Sent by the council to investigate the distress call from the Alchemor, Jazz landed not far from the scrapyard. Venturing in, he encountered Sideswipe whose attempts to challenge him were shortlived. After exchanging information with Bumblebee, Jazz found their reunion interrupted by the arrival of the Decepticon Ped. The Autobots pursued Ped underground, and Jazz was paired with Sideswipe. The pair found Ped's hideout, and were soon face-to-face with Ped himself. Jazz used a ruse to draw information out of Ped, but during the subsequent fight, he and Sideswipe were buried in rubble. When they arrived back at the scrapyard, a plan was in operation to trap Ped. After a brief setback in which the Autobots fell into a pit, Denny Clay managed to fish them out with an electromagnet. Jazz was grabbed by Ped until Sideswipe managed to anger Ped into letting go of Jazz and grab him instead. Jazz helped Sideswipe fight Ped in the stasis pod and the pair succeeded as Ped was knocked into his stasis pod by Denny who used his crane. Jazz and Sideswipe fist bumped on their success. Before returning to Cybertron, Jazz promised he'd smooth things over with the council about Bumblebee.
Jazz is a relaxed, firm, fairly mature, and a friendly Autobot soldier. He is also capable of taking down certain enemies and can be deceitful to trap them, like he was able to trick and blast Ped. Jazz also appears to be a role model figure to Sideswipe, as he taught Sideswipe to not care about what others think of him, which Jazz used Ped as an example of someone who cares of what others think.