Ratchet & Clank (series, except for Secret Agent Clank.. bad PSP port)

Jak and Daxter (1, 2, 3, X)

Baldur's Gate: Dark Alliance (1 and 2 - Fun top-down hack & slash RPGs, great in singlplayer and co-op)

Drakan: The Ancients Gates (Sequel to Drakan: Order of the Flame on PC. Great action/RPG with dragon flying)

Champions (-of Norrath and -Return to Arms - Very similar to BG: DA... possibly some of the longest games on the PS2 - the sequel can take 100+ hours to finish)

Darkwatch (awesome 'wild west' FPS with vampires and undead.. some of the best split-screen multiplayer I've had on the PS2)

The Legend of Spyro (Trilogy. Didn't receive particularly good reviews, but they actually are quite decent action-platformers)

Metal Gear Solid (2 and 3. Fun action/stealth gameplay with a LOT of cutscenes)

Transformers (NOT the game of the movie, but rather the one released in 2004. Fun 3rd person shooter with large open areas to explore)

Metal Arms: Glitch in the System (Fun 3rd person shooter with platformer elements)

Forgotten Realms: Demon Stone (Good action-RPG)

Psi-Ops: The Mindgate Conspiracy (Great 3rd person shooter which allows you to use psychic abilities to solve puzzles and destroy enemies)