I didn't grow up during the golden era of the Ps2, so I can only speak for games that I replayed way after their original release date.
1. Shadow of the Colossus - no other game is like it. Amazing.
2. San Andreas - such a huge game. Technically was pretty good for it's time
3. NFL street 2 - not the best game but the fun factor is infinity
4. Need for Speed: Most wanted - Better on 360 but still my favorite racing game ever.
5. Dragonball Z Budokai 3 - OMG DEM FEELZ D:
Honorable mentions: Both God of War games, Kingdom Hearts, Vice city, Guitar hero 3