Pikman is a great suggestion but I've already beaten both of them. I played F-zero too, though I never finished the campaign, which I played on the normal difficulty way back when.

So I'm looking for a PS2 or GC game, (though I'd much rather it be on the ps2) that is very challenging in the mental and physical sense. Shadow of the Colossus was a good example of a game that required me to actually think about how I was going to accomplish killing each boss. Though peoples opinions of whats challenging will vary, hopefully that gives a general idea of what I mean. I'm pretty much open to any genre style except side scrolling old school 2D type games.

For me, if a game is not challenging, its not very fun xD

Any suggestions? :)

EDIT: I want to give a better idea of what I meant by hard... Hard as in... I can't figure out how to precede, and I almost want to grab for that strategy guide but I tell myself NO! I have to figure this out! I can do this! Not hard in the sense that my reflexes aren't fast enough, though it playing a role in the difficulty is important..