Here are some of my recommendations:
-SNES-Station -OMFGzzz, u can play SENS on teh PS@!!11 make your own cd at http://snes-station.gamebase.ca/index.htm
-Tekken 5 - just came out recently, super cool game and i assume ur a tekken freak like me from your avatar
-GTA:SA (altho its coming for pc soon but its better on the big screen)
-Burnout 3 - now im not a fan of racing games but this game is so awesome, believe me. most fun you'll ever have with a racing game.
-Naruto Narutimate Hero 2- fun if youre a naruto fan
-Winning eleven 8 -most fun youll have with a soccer game, especially with two multitaps with 8 players @_@
-Soul Calibur 2 - another fighting game worth mentioning
-DBZ budokai 3 - yes, i actually fun with a dbz game *gasp*
oh and one great application you cant forget is ps2reality media player. basically itll allow you to: listen to mp3s, view jpeg images, and best of all watch divx/xvid encoded avi files on your ps2! its what i use my ps2 most for. well discs are swappable and it can read avi files from any cd. only downside is that sometimes the video lags so your really taking a risk everytime you burn a movie and checking if itll work on your ps2. if the results are postive, it turns out to be way better than a vcd player. well heres the link- http://ps2r.dg2.org/
also, any questions about ps2 can be answered at www.ps2newz.net , great helpful forum although there are the occasional people on their periods. hope that helped ;D