Tough call, considering how robust and diverse the PS2 library is, you might as well just do a "TOP n" listing. But some of my faves I can say for sure…
Dragon Quest VIII
–This made a previous list of mine in the "Top 10 favorites" thread, and it still holds true. A grand colorful world, lots of exploration and things to see, a strategic battle system, and a beautiful soundtrack make it a must play.
Virtua Fighter 4
–Also on my top 10. Simple interface, complex fighting system, and a robust training mode that has yet to emulated in other fighting games.
–The PS2 port of this game is actually quite good. Damn good. Really gave me the experience of the HL universe and gameplay when I lacked a "proper" PC and interface on which to play it. Theres a lot of secrets and extras too, including the co-op mode Decay and Alien mode.
Metal Gear Solid 3: Snake Eater
–Everything gameplay wise that defined MGS2 without the bullshit. I also got a kick out of the survival elements were fleshed out, CQC, and quite possibly the one of greatest boss fights (if not, THE) in the history of forever (The End).
Grand Theft Auto: Vice City
–Yeah, I know GTA probably ain't the most popular thing on these boards, but I honestly had some of the best times with this games. I loved the 80's setting, the Miami motif, the extra mechanics and vehicles that I had wished were in GTA3, and of course Ray Liotta yukkin it up as the humorously sociopathic Tommy Vercetti.