|MadSci Network: Astronomy|
This turns out to be a really tricky question, simply because we haven't found enough planets outside of out solar system to really get a handle on how common planets are. Here's sort of the best guess:
Current theory is that planets form along with stars as sort of a natural by-product of star formation. So we'd expect planets to be common around stars, at least whose formation took at least as long as it takes to form a planet (not all necessarily would). But to get a good idea of how common they really are, we need to examine a lot of stars and either find planets or convince ourselves that none exist. Since we've only been finding planets outside our solar system recently (in the past 5 years) and since we still can only find fairly large planets with small orbits, we are a long way from achieving this goal.
This doesn't stop astronomers from making guesses, though. We are really interested in this, since the number of planets in our galaxy affects the chances that we might find life elsewhere. Some astronomers think that nearly all stars have at least one planet. Others think that as few as 1 in 10 or 1 in 100 might be a better guess. Since there are 100 billion stars in our Milky Way galaxy, this means that the guesses would expect there to be between 1 billion to 100 billion stars with planets.
You also need to guess how many planets are found around each such star. Our sun has 8 or 9, but we might have more or less than normal. I'd guess maybe between 1 and 5 planets/star-with-planets, so I'd guess between 1 billion planets and 500 billion planets.
Bear in mind that these numbers are really only guesses, and we have almost no evidence for any of them. There are basically just astronomers guessing according to what they'd like there to be (some of us want lots of planets, of course, so our guesses are probably too high).
If you want to read more, try "Astronomy Today" by Chaisson and McMillan or "The Cosmic Perspective" by Bennett, Donahue, Schneider and Voit. Both textbooks have sections about this (and I'd expect most introductory astronomy texts would, as well).
Sorry the numbers are so vague. Stay tuned, because I beleive that we will be able to improve these guesses a lot in the next few years as we find more planets outside out system!
Try the links in the MadSci Library for more information on Astronomy.