Planet Earth(main planet)-This is where all the fighters are currently located.This planet has its own set of Dragon Balls but they aren't very powerful.This planet has no specialty.
Planet Namek-Home of the Namekian Race.This planet has a set of Dragon Balls that are rather powerful.This planet will alos be used for the first tournament.It has no specialty.
Planet Vegeta-Home of the Saiyin Race.This planet is a good planet to go to if you want to train.You can go there and fight some Saiyins to gain some levels.It has no Dragon Balls and serves the special purpose of workin up your Level,Strength and Fighting skills.
Planet Neo-Vegeta a.k.a. Tasbar-One planet,two names.This is Bardocks home planet and home to Saiyins.You can travel here also to fight more Saiyins if you want,but these Saiyins are going to be a little bit tougher.This planet has the special purpose of,you guessed it,Training
Planet Trabia-This is a planet north of Namek.It has its own set of Dragon Balls that are just,if not more,powerful as the Namekian set.Other than its Dragon Balls,this planet serves no special purpose.
Planet Harmony-This is a planet south of Namek and as you can tell by its name,it's a peaceful planet.This planet,other than peace,serves a special purpose.All the people there have healing powers and for 500 zenny,you can be healed completely in seconds.
King Kai's Planet-This is the home of King Kai.When and if you decide to go and take the training,you will travel here and train with King Kai.As you can tell,his small little planet serves the prupose of training.Although most people were defeated when they went there,I'll cut the rerst of ya some slack.
More Planets to come.Be patient and wait.Until then,Enjoy!