Gogeta Character Facts

Gogeta is formed by the merging of two mighty Saiyans, Vegeta and Goku, via the Fusion Dance. He is the second fusion performed through the Fusion Dance during the Dragon Ball Z series. 
Gogeta wears the same clothes that all creations of the Fusion Dance wear. However, Gogeta's vest has a different color scheme than Gotenks'. The padding around the neck and shoulders of the vest is reddish orange rather than yellow, and the vest is either a very dark blue or a dark gray, rather than the lighter blue vest that Gotenks wears. The hair is very similar to Vegito's, with the only differences being that Gogeta only has one free hanging lock of hair instead of two and Gogeta having Vegeta's widow's peak. Gogeta also acquires Goku's peach like skin rather than adopt Vegeta's more mild tan. Gogeta possesses Goku's body structure as he is tall and slender, but he seems to mostly possess Vegeta's facial features. 
Although they are made in a similar way, Gogeta has personality traits that are different from Vegito, though it is impossible to tell which counterpart's personality is the dominant one. Since his appearances have been limited and short, it is difficult to tell if his personality is a composite of both Vegeta and Goku (Vegeta's seriousness and Goku's sense of justice) or a completely unique personality. At Super Saiyan 4, it would seem that his personality is like that of Vegito. He enjoys toying with his enemies and pulling pranks.
Veku is the fat version of Gogeta who occurred when Vegeta and Goku attempted to fuse for the first time. He is one of several failed fusions present in the series. Vegeta fails to extend his index finger, resulting in an embarrassingly weak fusion which forms a fat fighter called "Veku" by South Kai; a name that comes from Vegeta and Goku. In this form, speed is decreased, and ki is extremely limited. Because of his state, Veku is does not perform any ki attacks due to the large drop in power. Also, because of his fat body, he does not retaliate by punching and kicking. Instead, all he does against Super Janemba is pass gas and escape using what he calls his "Rabbit Feet" technique. Just like a regular fusion, the time duration is 30 minutes before the two fighters defuse. This type of failed fusion is also seen in Goten's and Trunks' during the Majin Buu Saga, where they formed Fat Gotenks when attempting to fuse for the first time. 
Immediately after the successful fusion of Vegeta and Goku, Gogeta is at Super Saiyan as both halves (Vegeta and Goku) had previously mastered the transformation.
This form is seen in Dragon Ball GT, where Vegeta and Goku both faced off against Omega Shenron as Super Saiyan 4. With the Fusion Dance, they successfully created the powerful Super Saiyan 4 Gogeta. Unlike Vegeta and Goku's Super Saiyan 4 forms, Super Saiyan 4 Gogeta has brown fur and fiery crimson hair, instead of the opposite, and he is the only Super Saiyan that features blue eyes (without a strong green hint) as well. He is also the only character in the series with glitter in his energy aura. Compared to his more serious form, Super Saiyan 4 Gogeta is somewhat more playful and cocky (almost akin to Vegito's attitude), toying with the evil Omega Shenron instead of easily defeating him, possibly because the power was going to his head, though Vegeta states that Goku was in fact responsible for this behavior (however, it could be possible that Vegeta was merely shifting the blame onto Goku). It could be implied that Gogeta's personality may be based on a combination of Goku's youthfulness and Vegeta's arrogance, though this is only speculation. It is also implied he was only doing this so Omega Shenron would use his Minus Energy Power Ball attack, which Gogeta could use to fully cure the planet of Omega Shenron's evil energy. This is likely, as Gogeta immediately tries to destroy Omega Shenron afterward. His speed in this form is the greatest seen in the series, being so swift, not even the viewer is able to see his movements. As an example, he is able to knock Omega Shenron away with what appears to be impossible to see blows, which are shortly later revealed to be three, almost simultaneous strikes. When Gogeta said he would slow down in his attacks so he could "count em' this time", those same strikes appear as simple twitches, if anything. Along with his unbelievable speed, Gogeta also harbors an extraordinary amount of power and energy. As a Super Saiyan 4, Gogeta is seemingly invincible due to the massive power level gap between him and all other warriors in the series. His only weakness is his inability to stay fused for longer than 10 minutes due to the abnormally huge amount of power he possesses, which ultimately led to him de-fusing before he could deliver the final strike to Omega Shenron.