Hm, hard to say, as I love so many...
But if I were forced to whittle a list down:
Star Wars: Knights of the Old Republic
Godhand
Space Channel 5
Powerstone 2
SoulCalibur
Twinkle Star Sprites
Gitaroo Man
vampire Savior
Um Jammer Lammy
Guilty Gear X
Super Ghouls N Ghosts
Chrono Trigger
Guild Wars
Herzog Zwei
Heavenly Sword
Castlevania SOTN
Tekken Tag
Culdcept
Bust a Groove 2
Advance Wars
Ikaruga
Zombies ate my Neighbors
Saturday Night Slammasters
Archon
Wrath of the Black Manta
Skate or Die 2
Rainbow Six Vegas 2
I can't them in order, but those are a few of the games that I loved playing every second of, had high replay value and that I went out of my way to get other people to play. These are all games that inspired me to either compete, have long sessions where I'd stay up all night playing, or play all night with friends.
Also props to Jaxel on mentioning Beyond Good and Evil, great underrated/unacknowledged ps2 game and an honorable from me.
cha cha