Well, I own both a GameCube and PS2, but avoid the X-Box like the plague.

Microsoft, you understand...anyway: -
The GameCube is very good. It has stunning graphics, cute discs ( [img]tongue.gif[/img] ) and is extremely compact. Moreover, the old cable for the TV is compatible, if you owned an N64. The games themselves vary greatly, and you can't really judge a console by the games anyway...but there are a great many good ones out there. Also, following the trend of the N64, it supports 4 players rather than the PS 2 player only. Oh, its cheap now too, cheaper than a PS2 here in the UK (may be different in the US). One problem I've heard of is that it overheats easily because of an inefficient fan, but I haven't had any problems, and I have left it on for over 4 hours.
The PS2 is great too, backward compatible with the PS1 and has great graphics as well. It is a little heavier and bulkier than the GC, but boasts a larger variety of games available as well as popular classics like Final Fantasy, Metal Gear Solid, Tekken etc. Plus it's a DVD player which can make it a better choice than the GC, but it only supports two players. Another bonus to the PS2 is that you will only ever need one memory card (all 8MB) for the PS2 games, maybe two if you have over 10 games. [img]tongue.gif[/img] Seriously. The official GC memory card, being only 4MB, won't last long. I recommend getting an
unofficial memory card at 16MB, which should be enough. And I emphasize unofficial simply because both official controllers and memory cards are at ridiculous prices.
I'm not sure what I'd rather go for personally, but I did have the PS2 first (mainly because it came out first) but I haven't regretted the investment in the GC. I guess you'll have to make up your own mind on the actual choice, I hope my answer helped!
PS: Oh, the X-Box is bulky, heavy, the controller is uncomfortable and most games are available on PC shortly after being released on the X-Box. Yes I loathe Microsoft.