Well, it all depends on your favorite genre of games. However, I'll see what little insight I can give you.
My personal rankings are like this:
1) Gamecube
2) Playstation 2
3) X-Box
Now, hear me out. If you are only interested in the short-term gaming, as in a month or two and don't want to wait for good games, than the Gamecube is definitely not for you. Most of the Cube's star games are coming out towards the end of summer and the Fall. So, if you aren't one who likes to wait, than I would go with the PS2.
Now, the PS2 has the largest selection of games, not to say they are all good, but the largest none the less. Personally, my favorite type of game is the RPG. However, my personal opinion is that most recent RPGs have been lacking when compared to the genius of the past. That is why the Cube beats out the PS2 for me. But, if you like a lot of 3rd-party games, then the PS2 might be for you.
Now, contrary to what many say, and probably will say, the X-box isn't all that bad. Personally, Halo isn't my cup of tea, but I know many people who like it a lot. Plus, the X-Box is the most technilogically advanced system when you look at the specs. Not to mention it has the capital to back it up. It does have some interesting games, and some 3rd party support.
So, I would go with a Cube, mainly for games like Resident Evil, The upcoming Mario, Zelda, and Metroid titles, and Capcom VS SNK 2 EO (Beach Spikers LOOKS good too, if you catch my drift). If you want a large selection now, than I'd say the PS2 would be your best bet. But, if you see plenty of games you like on the X-box, you choice may lay there. I hope this has helped you out.