episode 213
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Depend on which version of Goku you're speaking of: Goku SSJ1 vs Majin Vegeta: Majin Vegeta Goku SSJ2 vs Majin Vegeta: Equal Goku SSJ3 vs Majin Vegeta: Goku Goku SSJ4 vs Majin Vegeta: Goku
on mega video episode 230
Majin Vegeta. Majin Vegeta vs SSJ Goku (Ascended) ended in a draw, therefor one can conclude that an SSJ2 Goku would beat Vegeta.
they fuse in episode 253 of dbz thanks for the question
If you are talking about Vegeta as a kid, I have seen him fight in the movie-Bardock-the Father of Goku (if i remember correctly). If you are talking about Vegeta Jr. (the great-grandson of vegeta), he is seen fighting Goku Jr. in the last episode of Draghon Ball GT.