Gogeta is formed when Goku and Vegita do the fuion dance. Gogeta didn't really appear much in the DBZ series. He only appeared once and that was in the special movie 12. The fusion process was rather short, and Gogeta easily defeated his nemesis, so there really isn't much to say about him. Later in the GT series, Gogeta returns as Goku and Vegita fuse again as SSJ4 to form Super Saiyan 4 Gogeta, the most powerful character in the DB series that was ever created.
