Gogeta's History
Fusion Reborn
After Goku successfully defeated the first form of Janemba, he struggled to defeat the demon's second form, even with help from Vegeta. Seeing no other option, Goku proposed they try using fusion and though Vegeta didn't like the idea at first, he agreed.
However he failed to do the technique exactly right with Goku, resulting in the two of them fusing into the short, weak and obese Veku. He was, obviously, no match for Janemba and was forced to run from the demon's assault for thirty minutes, stumbling around and farting in defense. Just as Veku was cornered and about to be finished off by the demon, the fusion time ran out and Goku and Vegeta defused. After an hour, they attempted the fusion again, while Pikkon distracted Janemba and succeeded, fusing into the powerful Gogeta. Demonstrating his great strength, the fusion easily defeated Janemba and destroyed him with the Starbust Breaker attack. As the negative energy that gave birth to the demon dissipated, the ogre, Saike, was left behind. Upon making eye contact with Gogeta, the ogre ran off in fear of the mighty warrior, which made him chuckle, before he defused back into Goku and Vegeta.
Dragon Ball Super: Broly
While Goku and Vegeta left Frieza to deal with Broly, they and Piccolo were stratagizing a way to defeat the mindless Broly. Goku and Piccolo performed the Fusion Dance concept to Vegeta. The two Saiyans failed it two times (creating Veku and the scrawny version). They've succeeded on the third attempt and returned to the fight (saving Golden Frieza's life), Gogeta and Broly instantly clashed with Gogeta holding an edge when he turns Super Saiyan (while managing to acidentally rip apart the timespace continuum in the process). Gogeta was forced to assume Super Saiyan Blue to completely dominate Broly at full power and almost killed the latter with a Transcendant Kamehameha Wave, if Cheelai hadn't used the Dragon Balls to save Broly's life at the last few seconds.
Gogeta stops Frieza from destroying Cheelai and Lemo's spaceship, the space tyrant retreats and promises to return and wreak vengeance. Gogeta presumably defuses after this, since only Goku visits Planet Vampa to commend Broly for his potential (whilst becoming friends in the process).
Dragon Ball GT
After Goku couldn't beat Omega Shenron, despite being in Super Saiyan 4 form, Vegeta, who just became a Super Saiyan 4 thanks to Bulma's Blutz Wave machine suggested they try using fusion and Goku found it funny he was the one suggesting it. While Gohan, Goten, Trunks and Majuub fought Omega Shenron to keep him busy, Goku and Vegeta performed the Fusion Dance, becoming Gogeta once again.
Now in Super Saiyan 4 form, Gogeta was easily able to fight the united Shadow Dragon, even toying with Omega Shenron and eventually taunted him to the point that he used his Negative Karma Ball to try and destroy Earth. Gogeta combined the ball with some of his own positive energy as he kicked it away into the atmosphere, causing the entire ball to change into positive energy. It resulted in a nuke-sized explosion, which reversed all the negative effects the Shadow Dragons had caused to the Earth. Eventually Gogeta blasted Omega Shenron with his Big Bang Kamehameha, forcing him to revert back to Syn Shenron. But as he prepared to finish the Shadow Dragon off with another attack, the fusion time ran out early (it only had been 10 minutes or 15 at the most). This was because of the enormous amount of power the Super Saiyan 4 form used and Goku and Vegeta defused, though Goku was able to destroy Omega Shenron later on with his Universal Spirit Bomb.
