Dragonball is japanese animation (anime) created by Akari Teriyama. In Japan it was one of the top shows for a very long time. Today, in America, it is starting to get very popular, from the "Cartoon Network Toonami." Children watch it everyday, yet they no nothing of the real dragonball. Dragonball was originally a dirty and bloody cartoon, with characters who curse more than Chris Rock!! The fighters don't die in a puff of smoke; usually their heads pop off, there is a hole in there body, or they just get all bloody.
Dragonball starts out with a boy named Goku. He is extremely strong, and he has a real tail (how odd, is he human?). Two dragonballs belong to him. One day when he was walking home, a girl comes with a car and shoots him. Her name is Bulma, the daughter of the famous inventor of "Capsule Corp.", Dr. Briefs. Goku, amazingly, survives, and destroys Bulmas car. They get to knew each other, and start to search for dragonballs and meet many people, who they befriend. Their adventures are known as "Dragonball."
Dragonball Z starts at a fighting tournament. Goku and the gang are all grown up, and Piccolo is back. Goku and Piccolo make it to the finnals. Piccolo wants to kill Goku, but Goku beats the shit out of him. Out of kindness, Goku gives Piccolo a senzu bean to restore his strength. The tournament is over. One day Goku desides to visit Master Roshi with his son, Gohan. Raditz, a sayain, comes to find Goku, known to him as Kakorot. Goku learns he is a sayain, but won't join Raditz in taking over the world. Therefore, Raditz takes his son. Piccolo arrives, and wants to help Goku defeat Raditz. They rescue Gohan, but Goku dies. Dragonball Z goes until after the Majin Buu Saga, in which all the sayains become Super Sayains.
Dragonball GT happens after DBZ when everyone is grown up and has children. I really don't know a lot about it, because i haven't seen it.