Final Fantasy X; Deus Ex: Conspiracy; God of War I and II; Prince of Persia (all); really just any square-enix game--another fav of mine is Star Ocean 3.
Mortal Kombat Annihilation Dark Cloud Soul Calibur 3 Star Ocean: Till the End of Time Dynasty Warriors 5 Empires Resident Evil 4 Unlimited Saga Viewtiful Joe 2 Harvest Moon: A Wonderful Life Special Edition Those are basically the ones that I enjoy the most in my PS2 collection.
Games that gave me the most lasting impressions were: Final Fantasy X - Such a great story... tears at the end! Metal Gear Solid 3: Snake Eater - Classic Hero and sacrifice journey Resident Evil 4 - Leon kicks some ass! NFS: Underground - arcade racing at it's finest. GTA: Vice City - nice... Farenheit - Finished in two days, 8 hours total, but what a story!
Oh man..Alright lets sort the games RPG: Shin Megumi Tensei series (DDS, Nocturne, Persona 3) Final Fantasy X Disgaea series Atlier Iris Harvest Moon Fighting: Marvel Vs Capcom 2 Guilty Gear series Soul Caliber II Action: Mobile Suit Gundam Seed Destiny Plus: Federation Vs Zaft 2 Katamari Demacy series Metal Gear series
fighting: street fighter anthology .. has the classic street fighter II from super nintendo .. plus street fighter 3 . action: god of war racing: gran turismo RPG: final fantasy stealth: metal gear solid sports: EA games are pretty decent
The PS2 had an awesome library. Final Fantasy X, XII, Kingdom Hearts 1, 2, Xenosaga 1, 2, 3 Metal Gear Solid 2,3 haha I got addicted to Hot Shots Golf 3 for a period of time too