Well if you like sports game then this will be easy, some of the best football games ever recently came out. The new Madden 2002 by EA and the new NFL Fever by MS are awesome. Madden is on both PS2 and XBox, with NFL Fever on just XBox. If you have an XBox you might as well get the latter, and I would suggest NFL Fever, which was made ground up just for the XBox. Also a plus is XBox has 4 controller ports out of the box, so you dont need an adapter to play with 3 others.
The 'NBA Live' games for all systems are good. BUT! A fun-as-sh!t arcase-style basketball game is NBA Street for the PS2. This game is a lot of fun.
As you know the UFC games are coming out for PS2/XBox and Pride for all systems.
Then there is Boxing. Put simply, there is only one game to get, and that's Knockout Kings 2002 for XBOX!! If for no other reason than I'm working on it. But this sh!t is fun, its brutal and it can get bloody (I made sure of that last one myself). I'll post some screens later if I can. Its out late Feb I think.
For car racing games, Gran Turismo 3 for PS2 is tops, hands down. There really isn't much else. Project Gothem for XBox is really fun, too.
Not a racing game but chalk full of crazy driving and mad stunts and car-jacking is Grand Theft Auto 3, which I'm sure you know about, real fun.
Action games: Devil May Cry for PS2 is fukking awesome! Halo for XBox is one of the best games I will ever play, you HAVE to get Halo even if you only somewhat like first person shooters like Half-Life, Quake, etc.
As far as Resident Evil goes, there is a port of the Dreamcast RE, which is good, but for the most part you are sh!t out of luck. The RE series is now exclusive to GameCube (they are looking SWEET too). There IS however a Dino Crisis in the works for the other systems. But you know what, if you liked the RE series then you will love Devil May Cry. They are both from the brain of the same designer, in fact DMC was originally going to be Resident Evil 4, but because a whole new game. Much more action than RE, though.
Similar style to RE and Dino Crisis is Onimusha for PS2. It's made by the same company as RE and Dino Crisis (Capcom), and plays similar, but in Fudal Japan, like Samuri style. It's older now, but Onimusha 2 is coming out for XBox and I believe PS2 as well.
Beyond catagory is Metal Gear Solid 2. This one takes some patients, and moves slower, but if thats your thing, than it's the sh!t.
Those are off the top of my head. I'll let you know if anything else pops up.