Not a lot of puzzle games mentioned, I notice. Puzzle Fighter and Spin Jam for the PSX, and The Next Tetris if you're a *tris fan. Also, Worms Armageddon is good stress relief (I have a post to edit now, curse you... me!)
If you're into CV, get Symphony of the Night (PSX) and Curse of Darkness (PS2). Lament of Innocence is hit-or-miss, though I don't remember specifically why.
Other PS2 games to consider are Atelier Iris 2 and 3, Guitar Hero 1, 2, and 80s (yes, I know it has no bonus songs and "Metal Health"'s guitar solo was neutered, but I don't care), Rez, We Love Katamari, and Wild ARMs 3 and 5.