Planet Arlia - This Planet wasn't mentioned in any of the series at all, just in one episode. This is the Planet that Vegeta and Nappa wiped out before the go to Earth (while hearing about the dragonballs through Raditz's scouter).
Planet Earth - This planet is where most of the fighting takes place. It contains the weakest fighters in the universe (average). This is where the Z Warriors and their friends and family settle. These battles kill many, and at times, the Earth is blown up, but restored by the dragonballs.
Planet Freeza #79 - This is one of Freezer's many planet bases. This is the base where the Ginyu force is launched from and where Vegeta is healed after the fight with Goku on Earth.
Planet Plant - This was inhabited by the Tsufuru-jins. It was then conquered by the Saiya-jins, and renamed Planet Vegeta, until it was blown up by Freeza.
Planet Namek - This is the home planet of the Namek's. It was the home of the dragonballs and Picollo and Kami. This is also the planet where Goku and Freeza battled in which Goku reached SSJ level. It was also blown up by Freezer.
Big Ghetti Star - This planet is shown in Movie #6, where Koola was regenerated by the help of this star or planet.
Planet Vegeta - This was originally Planet Plant, but was captured by the Saiya-jins and then later Freeza destroyed it (along with all the Saiya-jins, except Goku, Vegeta, Brolli, Nappa, Radditz, Paragas, and Tarlaus).
New Vegeta - Founded by Paragas, the new Planet Vegeta is where Movie #8 took place. This is the place where Brolli and the rest of the gang battled in.
New Namek - After Old Namek was destroyed by Freezer, the Nameks and the Z Warriors wished for a New Namek. This is where the Namek's resettled.
Maykio star - This was the birth place of Garlic Jr. and once it reached earth it gave Garlic more power. The star brings out all the evil you've tried to keep bottled up inside
Planet Yardra - Very shortly mentioned in the DBZ series but this planet was where Goku travelled when he escaped from Namek. He learned the famous Instant Transmission technique.