Due to time-constraints, I usually stick to the sports game because I can just play a game here and there when I have free time. My absolute favorite is the Winning Eleven 7 soccer game from Konami. I am absolutely addicted to this game, and it is essentially all I play now. You'd probably have to be a soccer fan to get lots of enjoyment out of it, though. Otherwise, NBA Street Vol. 2 and Madden 2004 are solid sports games.
I'm too busy with work and other things to play some of the longer, more drawn-out games, but I did find Jak and Daxter enjoyable. Of course I probably played it for like 30 hours and got about 20% through the game. Way too much focus required. Same thing with Grand Theft Auto. Way too much time spent for little progress. Ace Combat 4 is a really cool flight combat game. The LOTR games seem to get good write-ups.
I am link-challenged, but here is a link to a good site to get general ratings on PS2 games:
http://www.metacritic.com/games/ps2/
