He is the prince of the Saiyan race, who was forced to serve Frieza and was spared the destruction of his home world. Being raised by Frieza made him a dangerous warrior. Vegeta's true motives for his villainy came from his desire to destroy Frieza and eventually rule the universe.
However once Frieza is defeated by Son Goku Vegeta decides to live on Earth and eventually falls in love with Bulma and marries her and has a son named Trunks, redeeming him to an anti-hero. Near the end of the series, he gains a daughter, named Bulla. In the OVA Yo! Son Goku and His Friends Return, it's revealed he has a little brother named Tarble whom he gets along with, even though Tarble doesn't have a fighter's instinct like most Saiyans.