Grand Theft Auto: Vice City: Loved it even more than GTA III, and I didn't even think that was possible. I don't know if it is the locale, or the fact you get awesome motorcycles and military helicopters, but it was just one of those games you could pop in and play for 20 minutes, or 5 hours, and it was still just fun. GTA back then managed to have a good story, while remaining laid back and silly. Always loved how Tommy would make hilarious snide remarks after being given a mission.
Jak & Daxter: The Precurser Legacy: While I found Jak II to be a little too GTA for my tastes(Ironic, since I love GTA), the Jak 1 was just pure platforming fun. Lots of locations with unique scenery, and all the levels really felt like a part of the same world, if that makes sense. One of the only games I've bothered to beat 100%, ranking up there with Mario 64 in terms of quality for me. Speaking of Jak, Jak X: Combat Racing is probably my favorite racing game ever as well. So fast, but also more Mario Kart-ish in nature, great combination.
Final Fantasy Tactics: Best Final Fantasy ever crafted, in terms of music, story, characters, gameplay, and everything else. I've ranted on this more times than I can count, so I'll just leave it at that.
Honorable mention: Call of Duty: Finest Hour. Got me into WWII shooters, and probably still my favorite.