Planets...
Planet Arila - This planet was mentioned in one Dragonball episode. This is the Planet where Vegeta and Nappa whiped out and are seen eating food over a fire 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 freinds and family live. This is where the Great World Tournaments take place.

Planet Freeza - This planet is one of Freeza's many planet bases. This is the base where the Ginyu force is launched and where Vegeta is held, after getting his ass kicked by the Z-warriors 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 Nameks. The dragonballs, Piccolo, Kame, and Dende originated from this planet. This is also the planet where Goku and Freeza battled in which Goku reached SSJ level. It was also blown up by Freeza.

Big Ghetti Star - This planet is shown in Movie #6 "Metal Kooler", where Kooler or Koola was regenerated by the help of this star or planet. It was later Destroyed by Goku and Vegeta.

Planet Vegeta - This planet was originally Planet Plant, but was captured by the Saiya-jins and renamed Planet Vegeta. Later on Freeza destroyed it (along with all the Saiya-jins, except Goku, Vegeta, Brolly, Nappa, Radditz, Paragus, and Turlaus).

New Vegeta - Founded by Paragus, the new Planet Vegeta is where Movie #8 took place. This is the place where Brolly and the rest of the gang battled in, but was later destroyed.

New Namek - After Old Namek was destroyed by Freeza, the Nameks and the Z Warriors wished for a New Namek. This is where the Nameks later settled.

Mayko Star - This was the birth place of Garlic Jr. and once it reached earth it gave Garlic his enormous power. It was destroyed by Gohan.

Planet Yardat - Shortly mentioned in the DBZ series, this planet was where Goku traveled to when he escaped from Namek. He learned the famouse Instaneous Movement technique from the residents of this planet.