I would suggest either Virtua Tennis game (there are 2 out for the PSP) if you're into sports games, they are really underrated games in my opinion but are solid fun with lots of replay value.
If you like stealth action games I'd suggest picking up Metal Gear Solid: Portable Ops or either Syphon Filter game. These are some of the best games on the PSP IMO.
If you want another racer, and are in to arcadey racing games I would suggest picking up either Burnout game (there are 2 out for the PSP).
If you like fighting games Tekken Dark Ressurection is high quality.
If you're looking for a good puzzle game I'd suggest either Lumines (there are 2) or Puzzle Quest (this one has some RPG elements for added depth).
If you like sandbox style games or brawlers I'd go with The Warriors and both Grand Theft Autos. Those are all quality.
For platformers I'd suggest Loco Roco, Daxter or Ratchet and Clank.
Sorry if the list is too long to help you in your choices, but I've played/owned all of these games except for Puzzle Quest, the second Burnout, the second Virtua Tennis, Vice City and the Second Lumines and can testify to their quality. They're all really great fun.
__________________
|