As someone mentioned earlier, it all depends on what you're looking for...
PS2 Pros:
- Immense library of games
- GTA, Tekken, Metal Gear, and Gran Turismo series are exclusive to PS2, for now
- Lots of RPG's, Final Fantasy being the most noteworthy
- Backward compatibility with original PS games
- DVD playback is possibly a plus (though I agree with one of the previous posters; if you truly want to watch a lot of DVD's, get a REAL DVD player. It's worth it.)
- Developers often use the PS2 as primary development platform (limits bad 'ports' along with some other smaller benefits)
PS2 Cons:
- Only 2 controller ports (though multitap is available)
- Hardware is noticeably weaker than XBOX and Gamecube in some multiplatform titles (blurry textures, jagged lines, etc.)
Gamecube Pros:
- Four controller ports
- Classic exclusive franchises (Mario, Zelda, Metroid, F-Zero, Sonic (it still feels odd saying that), etc.)
- Numerous strong party-game/multiplayer titles (great when you've got friends, not so great if you always game alone)
- Resident Evil franchise is exclusive, for now (except Resident Evil Online)
- Final Fantasy game(s) scheduled for 2003 release
- Much improved third party support in comparison to the N64
- Nintendo is arguably the best video game software developer in the world, in terms of quality and experience
Gamecube Cons:
- Alleged (misplaced?) 'Kiddy' image (it isn't half as bad as people make it out to be; people have a love/hate thing with Mario, so again it comes down to personal preference)
- Sometimes receives straight or sub-optimal ports (developers dont always utilize the hardware in multiplatorm releases to add and enhance features, and sometimes even sloppily port games, making them slightly worse than the original)
XBOX Pros:
- Four controller ports
- Most powerful console on the market
- Built in hard drive allows for custom soundtracks, save game storage, and more
- Usually has the best version of multiplatform games, in terms of graphics
- DVD playback is possibly a plus (see comments in PS2 section)
- Has recently scored some exclusive developers/licenses that could be potential hits (most notably Rare, and it will be interesting to how their games turn out after the buyout; 10% of the staff departed, and instead of Nintendo internally supporting their efforts, it's now MS)
- DOA franchise (not exactly my cup of tea, though I've heard some people really like those girls)
XBOX Cons:
- MS has yet to prove itself as a first-party developer, and currently lacks strong second-party support (And don't say Halo

Thank Bungie for that one, not MS)
- (+?) Has a PC-centric image (XBOX has an image of mainly receiving slightly watered down PC ports (Max Payne, Morrowind, etc), though if you don't have a nice PC, this could be counted as a benefit)
- Must purchase separate DVD kit for DVD playback
Note on exclusivity:
Even though a title may be exclusive to a console, it may be developed on the PC, as well (certain Final Fantasy titles, GTA, etc.)
Other Random Notes:
- Disc size is a non-issue. PS2 and XBOX basically use standard DVDs. The Gamecube discs are smaller, but by no means small at approximately 1.5 gigs. If extra space is needed, the developer simply creates a second or third disc at minimal cost.
- Controllers are a matter of personal preference, each having their highs and lows, though all feel fine after adapting to their individual quirks. The smaller S-Controller is recommended for XBOX, and Nintendo's wireless Wavebird controller is rather amazing. Also, adapters can usually be found to use alternate controllers from rival systems on your system of choice.
- Online gaming is still largely up in the air on all 3 systems. XBOX potentially has the best online plan, while Nintendo's is arguably the weakest, though this is all still mostly speculation in the grand scheme of things. Many factors are involved, and if online play is important to you, research each systems online plan thoroughly before making a purchase.
Personal opinions/recommendations:
It all comes down to what kind of gamer you are, what you like to play, and whether or not you already have a PC or another console system. Casual gamers should likely stick with the PS2 since it has such a diverse array of titles. Fans of Sonic (since Sega is now third party), Mario, and other classic/nostalgic franchises should go with Nintendo. XBOX has good shooters and racing games. Nintendo has good multiplayer and party games. Sony has good fighting games and RPG's. In general, you'll find that exclusive titles make or break a console purchase, so buy a system that supports your favorite games.
If you can afford it, buy two systems -- A PS2 or XBOX, and a Gamecube, as you'll get the least amount of overlap in titles. I own a GC (love the multiplayer games and Nintendo franchises) and a PC (for my FPS, RPG, and online gaming fix), and I'd like to pick up a PS2 sometime down the road. I have a hard time recommending XBOX simply because they don't have many great titles that can't be found on other systems or the PC. If MS can produce a strong holiday lineup, it could really turn things around for them, though.
In my opinion, skip over IGN, Gamespot, and such and simply head straight to gamerankings.com. They compile reviews from printed sources and sites all over the web. It's the best way to see if a title is truly good without testing it yourself since you receive a large sample of reviews. The larger sites, while nice, tend to be.... inconsistent with their reviews, since they deal with a large number of games, and reviewers vary in strictness and bias. You can easily be burned if merely rely on one or two sites.
Lastly, the best way to choose a console is to find friends that already own them, are very knowledgeable of what's available, are knowledgeable of what you like, and are willing to let you play (or borrow) their games. Research other titles you're interested in and rent a few of them. Whichever system you had the most fun with overall, well, that's your winner.