Ok, I know that at least one person on the forum is scratching his/her head at the word Dragonball. I, being a Dragonball Z lunatic, know very much about the DBZ series, and a little about Dragonball, and Dragonball GT (this is because Dragonball isn't available to me, and because GT stinks).
A basic rundown of the three: All three series are based on the mystical dragonballs, which can grant any wish to one person when all seven are gathered together. Sometimes, the bad guys wish to collect the dragonballs, and the good guys have to protect the dragonballs, or the bad guys are kicking the good guys all over the place, and the good guys use the dragonballs to their advantage, such as bringing a friend back to life.
All three Dragonball series are centered around the main character; Son Goku. Dragonball takes place when he is a child, Dragonball Z takes place during the prime of his life, and Dragonball GT takes place during his older years, although he has been transformed back into a child by the Dragonballs, a mistake made by an enemy who hadn't been seen since Dragonball.
That's basically the run-down of DBZ. Of course, I can't give away the plot in one post. That wouldn't be fun. Also, it would be a very long post. I, personally, hope to see this section grow really big.