Grand Theft Auto 3 is awesome!!! Look for Stunt driver this spring, from the same company. Also State of Emergency is coming out soon, where your main premise is to join a gang and cause riots. You even have the WTO in Seattle riot to partake in.
Metal Gear Solid is a fabulous adventure if you are into Spec Ops movies and books. Main premise of the game is that you sneak and peek with great Computer Artificial Inteligence. The programmers watched and learned from the British SAS in how counterterrorism tactics are employed. You see their work shine in the game as you try and avoid fire teams searching you out.
Tony Hawk 3 is fuggin' Awesome! That is if you are an old school skater like I am. Heck I even built a character that looks exactly as I did when I was in my heyday skating. Just overall fun even if you are not a skateboarder.
Ace Combat 4 is a quick but great arcade/simulation air combat game. Interesting scenarios in a psuedo country with realistic (for an arcadey style game) controls and weapons on the aircraft.
Gran Turismo 3, is alright if you are an import freak. But I do not think anyone here really is such. They do have the 2001 Cobra R, the Shelby Series 1 in the game and a few other American cars, but it is very one sided to the Japanese and Euro manufacturers. GT2 had muscle cars at least which made for mad fun.