Appearance

Gogeta wears the standard fusion dance clothing. The padding around his neck and shoulders are orange, and he wears a blue sash. He also wears black wristbands.
Personality

In his first appearance, Gogeta’s personality is completely different from Vegito’s personality. Gogeta is very serious and straightforward, as he quickly destroys the monster Janemba.
In GT, Gogeta’s personality is very similar to Vegito as he’s playful and flippant in his battle with Omega Shenron.
Plot
Fusion Reborn

Goku and Vegeta decide to fuse but the fusion is performed incorrectly, and thus creates Fat Gogeta (or Veku). Throughout the battle, Veku evades Janemba and defends himself by passing out gas. He later defuses back to Goku and Vegeta. Goku and Vegeta perform the fusion dance one more time, and this time the fusion is successful and creates Super Gogeta.
Gogeta quickly destroys Janemba with the Stardust Breaker. Janemba is later turned back into the teenage ogre and he runs away from Gogeta, who laughs. Gogeta later defuses, and Goku and Vegeta bid their farewells.
GT

SSJ4 Gogeta is created after SSJ4 Goku and SSJ4 Vegeta perform the fusion dance. SSJ4 Gogeta begins to overwhelm Omega Shenron. Omega, angered, attacks SSJ4 Gogeta with multiple energy ki blasts but SSJ4 Gogeta acts like nothing happened. This angers Omega even more. SSJ4 Gogeta starts toying with Omega Shenron, and even pulls a prank on him with the bluff Kamehameha technique.
Omega Shenron, tired of this, decides to destroy SSJ4 Gogeta and everyone with the Negative Karma Ball. He creates the ball and launches it, however SSJ4 Gogeta casually kicks the ball out of Earth’s atmosphere. SSJ4 Gogeta powers up a Big Bang Kamehameha and hits Omega Shenron. SSJ4 Gogeta powers up another Big Bang Kamehameha but, due to the time limit, defuses back into Vegeta and infant Goku.
Techniques
Stardust Breaker – This is Gogeta’s ultimate move in his Super Saiyan state. He attacks his opponents with punches and kicks, and then creates a multi-colored ball and proceeds to throw it at his opponent which utterly destroys them.
Big Bang Kamehameha – This is Gogeta’s ultimate move in his SSJ4 state. He powers up and blasts an extremely powerful blue beam at his opponent.
Transformations
Super Saiyan

Gogeta has a strong resemblance to Vegito in this form. His hair is golden and his eyes are emerald green. He has only one bang, while Vegito has two. Gogeta also has a yellow aura around him.
Super Saiyan 4

In this form, Gogeta has red spiky hair and blue eyes. He also has dark, red fur around his body. His aura has glitters.
Powers and Abilities

Gogeta is an extremely powerful Saiyan. In his Super Saiyan state, he is able to easily defeat Janemba who was dominating SSJ3 Goku. In his SSJ4 state, he was far above Omega Shenron that he dominated him and was not even taking the fight seriously.
Matter Manipulation/Magic – while it is not stated which one it is for sure, we do know that Gogeta can materialize objects out of nothing, during his fight against Omega Shenron he summons a confetti shooter out of nowhere, meaning that he can either manipulate matter or do magic.