Well, tomorrow I'm going over to a buddy's house for a 10 hour or so "GameFest". Three TVs, One XBox, One GameCube, One PS2. So I'll give a final answer in two days
Initially, from reviews in gaming magazines and some personal inferences, I would rank them: 1) GameCube, 2) PS2, 3) XBox.
I pick GameCube first because of a game I am really looking forward to (Rogue Leader). Also, the graphics are good (which is pretty much true for all three systems), Nintendo has good depth in their initial games, and they have gone against the "Bigger is Better" attitude in the industry. I've seen their disks, and they're about half the diameter of a standard CD/DVD, yet the space is used well. Big things come in very, very small packages.
PS2 is next simply because it has already been established, and has a very good head start on games you can play on it.
XBox I picked Last, because the game depth is horrible, almost exclusively FPS type games (led by Halo, which certain XBox enthusiasts I know seem to believe will "replace that piece of crap Half-Life". That's a direct quote, based solely on seeing the graphics for 15 seconds
). The fact that it's **** huge, and might as well be a computer is another reason (I wouldn't be suprised if Microsoft releases something to add a keyboard and mouse to it). And from my experience, Microsoft never does anything right the first time around. XBox 2 will probably be great, but XBox is targeted on too small an audience. One of the main advantages it is trying to use against GameCube, the fact that it can play DVDs, is quickly lost in its audience, most of which already have either a PS2 or a DVD player.
Just my $0.02