Vegeta, Prince of the Saiya-jin, appears after the death of Raditz. He comes with Nappa to Earth in an attempt to gain immortality by wishing it to Shen-long. He appears first with brown hair (in the anime) and slightly different looks, but after a year, when he comes to earth, his looks are already the same as those that we see for the rest of the series(Vegeta seems to be about 10 years old in his 1 year space journey).
Vegeta finally joins Goku and friends but never gets to be a real allie; he's only purpose in life is to defeat Goku and prove that he is stronger.
During the series he slightly settles down with Bulma having with her two kids: Trunks and Bra.