More PS1 games:
Rollcage and Rollcage Stage II, Possibly one of the best ports I've seen the graphics are amazing for the system, the framerate is smooth and it's fun as hell. No One can Stop Mr. Domino!, nice puzzle game and you can get it cheap these days. Blast Radius, any of the Bust-a-Move games, Ace Combat Trilogy, Colin McRae Rally, Colony Wars, Brave Fencer Musashi, Doom (Actually one of the best ports of the game), Grandia, GTA 1,2 & London, Herc's Adventures, Intelligent Qube, Lemmings & Oh No! More Lemmings, Lunar and it's sequel, MediEvil 1&2, Tatics Ogre, and the Tekken Trilogy.
PS2 games:
Black, Aqua Aqua, Darkwatch, Beyond Good & Evil, Psychonauts (Xbox version is slightly better, but you're still getting the same experience here), Ape Escape 2 & 3 (Superb platformers especially 3), Micro Machines V4, Rayman Revolution, Rayman 3 Hoodlum Havoc, Robot Alchemic Drive, XIII, Xenosaga games, and the .hack games.