Damn it. It figures that I'd be the only GameCube owner on the whole freaking board.
The GameCube has several plusses in its favor. I believe it's the cheapest of the consoles currently available, at $99 USD. There's even a special edition of the Cube currently available that comes packaged with Metroid Prime, and a Bonus Disc with a demo and lots of preview material for Metroid Prime II.
The GameCube's graphics are middle-of-the-road; superior to those of the PS2, slightly inferior to those of the Xbox. The GC is also a small unit, and rather portable; it has a small handle on the back so you can carry it around with you, if need be.
The GC's biggest advantage lies in its total control of Nintendo-licensed products. While the GC gets a fairly healthy number of multi-console ports, it's the only place to play Mario, Zelda, Metroid, and Starfox titles. I bought my GC primarily to play Super Smash Bros. Melee when I purchased it a few years ago.
The GC is not without flaw, however. As far as I know, it doesn't have any online support (though this may have changed, I'm not sure), and a few of the better-known console titles aren't available for the GC; the new Star Ocean, for example, as well as the upcoming Godzilla-based fighter.
Despite that, I'm behind the GC all the way. My roommates on campus spent many a late night screaming at their televisions while playing Mario Kart, and I personally am looking forward to Starcraft: Ghost, Starfox II, Metroid Prime II, and Mega Man X: Command Mission.