Dragonball Z followed the hit comedy/action anime and manga, Dragonball. It was made by a great writer of anime, Akira Toriyama. Dragonball leads off from the Bardock special (picture of Bardock, Goku's dad to right).

Goku arrives at the earth and Dragonball basically tells about his early life. It ends off with Goku getting married to Chi Chi and having a son, Gohan. The series ended in the 1980's and then Dragonball Z followed. Personally, I like Dragonball Z the best. Dragonball Z starts off with Raditz (Goku's brother picture below), coming to earth, and fighting Goku and Piccolo.

The series goes on with many sagas where Goku and the other good guys, Z Fighters, fight increasingly stronger villains. After about 300 episodes, and many many fights, the Z Fighters end up being basically the strongest guys in the universe.

The Dragonball Z series ended in the early 1990's, but Dragonball Z fans hadn't had enough, they wanted another series, Dragonball GT. I don't know much about Dragonball GT, but I've heard it wasn't as good as the other Dragonball series because it wasn't made by Akira Toriyama. Toriyama sold it to another anime company to make, but they had different artists, and they just didn't do as good a job. GT ends with Goku absorbing the Dragonballs and becoming infinitely powerful.