The first response is the most valid. PS2 has by far the largest library of games. It has the largest library of great games, mediocre games and crap games. But still, it has the most good games of any system.
X-box is the most powerful (but many games don't really take advantage of it because they were originally developed for PS2). It also is the only system of the three to support dolby digital 5.1 sound in games, though PS2 supports it if you're watching DVDs

). X-box has Halo. Can be easily hacked.
Gamecube is more powerful than the PS2 in the sound/graphics department, but not as powerfull as X-box. Gamecube has Nintendo's first party development teams which have created more new videogame genres than most companies have created videogames. They are having a difficult time shedding their "kiddie" image, though they are trying -- plenty of adult fare. Oh yeah....word on the street is the Gamecube/Zelda bundle (comes with every Zelda from the original NES game to Ocarina of Time) will be on sale at Wal-Mart from 6am until 10 or 11 (or while supplies last) for $79.
edit: I'm retarded. I should probably mention that this is a day-after-thanksgiving sale. Don't just go in on any given day between 6 and 11 am. Also, if you're interested check your local Walmart. Last year the one by me decided to open at 5am instead of 6; and some are open all night, but who knows when they'll start giving people the good deals?
Wrap up:
PS2: Best chance that you will be able to play any given game. Also best chance that you will never run out of great games to play.
Xbox: Best chance your game will look and sound as good as it possibly can (keep in mind we are talking about mostly subtle differences, not like the difference between a PS1 and PS2 game)
Gamecube: Best chance your game will be made by Nintendo, which really is a bigger deal than it sounds.
Overall Winner? Probably PS2. That said, of the three I own a Gamecube cos I only buy about 3-5 console games a year and Nintendo is my favorite software developer. Comically, the next system I buy will probably be an X-box cos I'm excited about the modding capabilities. I still think that the PS2 is hands-down the must-have system of the three. Different people are just looking for different things.