If this isn't a hamster dance I don't know what is...
That said--
God of War I and II (love 'em both; mindless button mashers they may be but they're just so friggin' addictive and FUN; plus you can get 'em both on the cheap)
Final Fantasy X (as I stated in another thread, this is the game that got me hooked on both my PS2 and RPGs in general)
Ratchet and Clank-Up Your Arsenal (I haven't played the first two, but this game is definitely in the top three platformers I've ever played)
Shadow Hearts: Covenant (played all three in the series and this is the one that stands out for me; interesting combat system, excellent graphics and humor)
Silent Hill 2 (the first Silent Hill game I ever played, and still the best)
Black (FPS with BIG explosions and all the bells and whistles you could want)
Really there are just too many good games to list. I tried to give a sample of different genres for your perusal.
Right this second I'm playing Silent Hill: Origins, Star Wars: Bounty Hunter, Final Fantasy XII, and Kingdom Hearts II. Meanwhile my Wii, Gamecube, and Xbox are collecting a nice layer of dust...