I have all three big consoles and the GameCube is probably my favourite in terms of gameplay. They always seem to license long games.
Best features:
It has exclusive games which rawk like all of the Nintendo games (Mario, Zelda, Kirby, Donkey Kong, Pokemon etc etc etc) getting their very own games on the GC), and we all know Nintendo are gaming artists. They have also had some special excusives like Resident Evil 0, Star Wars Rogue Leader games (which are pretty awesome, even for non-geeks) and some others.
The graphics are excellent, better than the PS2. I'm not sure if it's up to scratch on the XBox though, although the GC is about a quarter of the size of the XBox (seriously).
It's easily portable. I can actually fit it into the back pocket of my jeans, but I could probably fit a whole person in there. (¬_¬)
Crapness:
They have the smallest selection of games of the big three, meaning there's not as much choice and some games which come out on the PS2 and XBox won't be on the GC (like the SD and RAW games, which own). The WrestleMania games always seemed out of date after a month or so.
Not many of your friends will have a GC, because it's not very ''cool''. They're morelikely to have a PS2, meaning you can't swap games or invite them round without buying another controller (which is a bit crap considering the best GC games have awesome multiplayers).
My favourite games for it are Mario Kart: Double Dash, Super Smash Bros Melee, Sonic Adventure 2, Tony Hawk's Underground and Luigi's Mansion. Call me a sucker, but I really like the Mario and Sonic characters and to be honest it's hard to find a good GC game without a Nintendo character in it. Even Soul Caliber's new version has Link from the Zelda games as a GC exclusive. And with Pokemon Colosseum coming out today, I'll probably get that. A 3D Pokemon RPG? Hella yeah.