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The short answer is: as many as Toriyama wants there to be. He just recently added a few, back in 2007 or 2008 I think, for some TV special. You can find it on YouTube.
Otherwise, I can think of about five or six from memory. Ones specifically stated include Earth, Namek, Vegeta, Yami (Planet of Yakon, beastly lizard servant of Babidi), King Kai's tiny planet (hey, it's technically a planet!), and that one planet with the bug-people that Vegeta and Nappa conquer on their way to earth.
Obviously there are some implied planets, too. King Cold, Freeza, and Koola gotta be from somewhere. Likewise with Puipui and Babidi's other servants. Babidi himself is from some higher realm in general I think, not an actual planet. Then there's Pikkon, of course. That's all I can think of off the top of my head, though.
So, for an actually answer, I'd say definitely ten or more. You'd have to find info from these old Dragon Ball compendium-type books that were released back in the 90's. I bought one back then, but it's all in Japanese, so it's of little help to me. Sorry! Hope this answer helps, anyway.