Gamecube is out of the question. I feel somewhat sorry for Nintendo, but the cube just doesn't have the superior power of the Xbox or the superior games of the PS2. I guess it can be good for kids who actually like playing Mario.
The Xbox, apart from being Microsoft which is a minus on its own, has a fairly superior computing power and a hard drive. The hard drive however is being used in such a limited way that it's hardly better than memory cards. Ask Morrowind players about this, Bethesda is trying as hard as they can to get an expansion or plugins for the Xbox version of Morrowind, and they just can't.
The Xbox does have a better hardware - so much indeed that Microsoft loses money selling it - but I just don't find any of the games that are currently out particularly exciting, save those that are also out for PC. Note that since the Xbox is so similar to a PC, it is fairly likely that many of the games out for Xbox will eventually be out for PC as well (Halo).
You need to buy a separate remote controller to use the DVD player, and the controller is too big in many's opinion.
Ultimately, there just aren't enough good titles around to buy me on the Xbox, and those that I can find interesting I either can play on PC (Morrowind, eventually Halo) or can find equivalents on the PS2 (any fighting game). The only reason I can see now for buying an Xbox is for putting a mod chip, a keyboard and mouse on it, installing Linux, and thus getting a fairly good and extremely cheap computer (and damaging Microsoft in the process, wow!)
The PS2 is less powerful than the Xbox but (the following sentence is IMHO, ok?) if it's fun you're looking for, as opposed to polygons, it's the deal. There are an incredible number of games, plus Playstation ones, and many, many of them are very good. They have originality (which really lacks in most Xbox games that I know of), playability, plot, and since a lot of people has the PS2 you can sell them after you're done with them.
The graphics are currently slightly below Xbox games, but I expect them to get significantly better as programmers get more experienced on using it (as happened with the PS1). OTOH, I can't see the Xbox's graphics getting much better for this reason, because it uses the well-known and used DirectX APIs and is probably already well exploited. But even if I knew that the relative quality would stay the same, I'd go PS2 all the same for the reasons mentioned.
The huge fan base (an order of magnitude more than either of the other consoles) ensures that many quality games will be made for a long time. The DVD player is there, no separate stuff to buy.
An additional note:
People say that the Xbox plays DVDs better but I sincerely don't know how so. Is the image better? Is the movement more fluid? Is it more user-friendly?
