Planet Earth - Also known as our earth, this planet is where most of the fighting takes place considering thats where all the main characters live! The battles faught here kill loads of people and eventually destroy earth.
Planet Namek - This planet is where Goku and Freeza fought, and Goku became a SSj. It was then destroyed by Freeza. It was also the original home for the Dragon Balls.
Planet Vegeta - Was Planet Plant, but was captured by the Saiyans and then later Freeza destroyed it along with all he Saiyans, except Goku, Vegeta, Brolly etc.
Planet Arila - You get a glimpse pf this planet while Vegeta and Nappa are traveling to destroy Earth. They then kill the ruler and destroy the planet in a short amount of time.
Planet Freeza #79 - Many head stations for Frieza's troops like Vegeta used to go to...
Planet Plant - This was inhabited by the Tsufuru-jins lived. It was then STOLEN by the saiyans and so they called it PLANET VEGETA. Although ironically it got destroyed by Frieza later on...!
Big Ghetti Star - First seen in Movie number 6. It is also where Koola was recreated by the help of this planet. But it was later destroyed by Goku and Vegeta.
New Vegeta - Not much known at all on this planet...but it was founded by Paragus. And then it was destroyed.
New Namek - After Old Namek was destroyed by Freeza, the Nameks and the dragon ball warriors (Gohan, etc.) wished for a New Planet Namek using the dragon balls, and much isn't known about this planet.
Makhio Star - This was the birth place of Garlic Jr. and when over earth it gives Garlic Jr, tremendous powers. It was destroyed by Gohan's power blast.
Planet Yardat - Not much mentioned in the Dragon Ball series but this planet was where Goku learned Instantaneous Movement (moving from one place to another also known as teleporting).