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This is such a common question, on every single Linux forum, mailing list, IRC channel, the lot. To this end, below are a few links which hopefully will help you choose the right Distro for you.
Note: I recommend *always* try a LiveCD of the distro *before* you install it. A LiveCD will give you a good idea of what it's going to be like to use, and wont do anything permanent to your system, unless you tell it to.

Right, after that note, here are some links:
1) Distro quiz: These two sites (here http://www.zegeniestudios.net/ldc/ and here http://polishlinux.org/choose/quiz/ ) have a quick quiz (each) which at the end will suggest a Distro for you based on your answers (and provide a link to the right site).
2) Distrowatch (here: http://distrowatch.com/dwres.php?resource=major ) Distrowatch has a listing (as the name suggests) of the various distros around, along with pros and cons for each (probably best to look at this after you have a couple of distros in mind).
3) The Linuxforums "Coffee lounge polls" (here: http://www.linuxforums.org/forum/coffee-lounge/57346-polls-special-threads.html ) - A good list of a few polls for: Favourite Distro; Best for Older systems; Servers; New to Linux.
4) Google (no link...) - Google is your friend. A quick search simply for "which Distro ?" turns up about 276,000 results (a bit daunting, but you get the idea). Try searching for a suggested Distro, and read some reviews.
5) Distro sites. - This may seem obvious, but it's something I've come across before; if you're thinking about using a distro (say Ubuntu) go to the distro's website and take a look, look in the forums as well, that's a good place to look to see the sort of support you'll get from the community.

So, that should do for now. Feel free to add to this with some more suggestions.
Please, however, don't post links to your favourite Distro; this isn't meant to plug your favourite Distro, but to help people choose one. (I accept that people are going to respond "but XYZ Distro *is* good for UserFoo" but again, that's not the point, start a new thread about that Distro. Post helpful posts, links etc. to help people find out information in here).

Penguin.