Go to this location and create a check list of games you might be interested in on each system (choose the console and 30 results):
http://www.gamerankings.com/itemrankings/simpleratings.asp
And make your decision from there.
Personally, I was in the same situation a while ago (getting a console) and got a Gamecube. And I've been a happy camper.
The primary problem with the X-Box is that you can play most of the top games on the PC. This is a good thing if you aren't willing to spend a lot of cash on a good system, but a bad thing if you already have a reasonable good machine. After all, X-Box games that are also on PC:
Halo 1? Check. KOTOR? Check. Riddick? Check. GTA? Check. Prince of Persia? Check. Splinter Cell? Check.
Some of these games can also be bought at a much cheaper price on PC.
Other than being a good console for people with subpar PCs, it also has some interesting exclusive titles or games that aren't on PC (Burnout 3, Halo 2, Fable, Ninja Gaiden) as well as X-Box Live which is fun in Halo 2 and offers some new content from time to time (although some companies, like Ubi Soft, are starting to charge money for it).
Gamecube has a sizeable amount of fantastic titles that you won't find anywhere else or if you do, they either haven't been released yet or will be downgraded some (as will be the case with Resident Evil 4, Viewtiful Joe also had performane issues on the PS2). In order of awesomeness:
Resident Evil 4
Eternal Darkness: Sanity's Requiem
Zelda: Wind Waker
Metroid Prime
Metroid Prime 2: Echoes (hard game)
Paper Mario: The Thousand Year Door
Viewtiful Joe
Pikmin 2
Note that I didn't list any racing or sports games, as I honestly don't care for them very much (and they can be found aplenty on the PC), also there are exclusives like that too, F-Zero GX.