As of right now, Vegeta does not have a brother; but he will. Get excited, because at the "Jump Super Anime Tour" there is going to be a short 35 minute film based off of the Dragon Ball (Z) storyline, written by Akira Toriyama himself. We are told that this film will feature Vegeta’s younger brother, and will take place two years after Majin Buu was defeated.
So where was the little guy during the actual story then? His father, King Vegeta, died a long time before the series ever started, sometime when Vegeta himself was about 10-12 years old. I am then assuming that these two would be about 10 years apart, cause he wouldn’t be Vegeta’s “little” brother if they were only a couple years apart. Anyways, the King must have implanted this "second prince" inside a girl that wasn’t his wife, and sent the child away to a random planet just like Goku. This is the only way I believe this would work out, without having to change the actual story.
I hope this short gets such high praise that Toriyama and Shonen Jump decides to make another Dragon Ball series. And if you need someone to write this Japan, I can be the next Toriyama.
[Via Canned Dogs]