Star Ocean: Till The End of Time (there's also PS1 games, but I haven't played those)
Phantom Brave
Xenosaga Episodes 1-3
Xenogears (PS1)
Shadow Hearts
Kingdom Hearts (I hate these games, but for some reason, my friends love them)
I have never had a compatibility problem with my PS2 playing a PS1 game.
*waits for someone to say that some super obscure game doesn't work on the PS2*
EDIT:
soniklife wrote:thanks for the feedback guys! i know right off the bat i wanted to check out the final fantasy, kingdom hearts, god of war and ratchet & clank games.
I could go on forever about how great the Ratchet and Clank games are, Every year that one of those games came out, I would spend about 7 hours a day palying on my PS2 (PS3 now) playing the game, trying to get every last weapon, gadget, upgrade, Gold Bolt, etc. Ratchet and Clank is my favorite console series. God of War is a great series for the PS2 as well.