Origin: Saiyan
Birth Planet: Vegeta
Current Home Planet: Earth
Saiyan Name: (Prince) Vegeta
Known Family: King Vegeta (father) deceased;
Bulma (wife);
Trunks (son);
Bra (daughter);
Eye Color: Black
Hair Color: Black
Special Attack: Big Bang Attack
Final Flash
Vegeta is the son of the former king, Vegeta. He is from, you guessed it, planet Vegeta, which used to harbor the warrior race called Saiyans, before it was destroyed by Frieza. Vegeta's arrogance couldn't possibly be matched by anyone in the universe. Vegeta first came to Earth with the Saiyan elite Nappa. They heard of the Dragonballs through their scouters from Raditz before his death at the hands of Goku and Piccolo. So, they headed for Earth to get the Dragonballs and make a wish to live forever.
Vegeta was beaten and spared by Goku, allowing him to leave. But, Vegeta vowed to return and take his revenge. But, this revenge would have to wait upon hearing that Frieza was on the planet Namek looking for the other Dragonballs. He went after Frieza, hoping to defeat the tyrant once and for all. But, his plan failed and he was killed, only to be brought back by the Dragonballs. He was transported to Earth, where he decided to live with Bulma in Capsule Corp (given they have enough room for an army).
After time passed, Vegeta and Bulma, both stubborn as ever, developed feelings for each other. Before the Androids came to terrorize Earth, thanks to Doctor Gero, Bulma gave birth to their first child, son Trunks. Vegeta grasped the power of a Super Saiyan when trying to flee from a planet that was being bombarded by meteors (feel free to correct me if this is wrong, my memory is a bit fuzzy). When Vegeta thought he wouldn't escape, he exploded in rage and began to sport the yellow hair and green (teal, whatever) eyes.
By the time Majin Buu was hatched, Vegeta had gotten used to life on Earth. Even after being corrupted by Babidi's evil powers, Vegeta discovered (after hitting the back of Goku's neck, making him go unconscious) that Gohan had supposedly died. He vowed to take revenge for him, and came to the conclusion that he had to sacrifice himself for the safety of his family. For the first time, Vegeta died for someone other than himself.
After the defeat of Majin Buu, Bulma gave birth to their second child, daughter Bra. Vegeta could very well be called a Z Warrior and friend to Goku (although he probably wouldn't admit his repsect for the other Saiyan).