I should note that I don't have a psp, so I can't tell you if these will run or not, but if I did these are the games I'd be playing:
1.)
Tomba!: Pink hair, run around hitting pigs with a blackjack or boomerang before you hop on them and toss them into other pigs. 2D platformer with some 3d elements and a type of mission based gameplay that equals hours of fun.
2.)
Tomba! 2: 2d gameplay, 3d graphics, and more of the same.
3.)
Klonoa: door to Phantomile: Probably the best platformer on the PSX. Also a '2.5D' game, you control a cat/rabbit thing with 2 moves: a jump and the ability to blow up enemies and grab them. Use these two moves to beat the game in different ways.
4.)
Threads of Fate: Simple action RPG with colourful graphics and two playable characters. Play as Rue, a male with the ability to turn into animals, or Mint, a female who can use magic. Rue's storyline is probably the main part of the game, with a more serious tone. Mint's, on the other hand, is more of a parody.
5.)
Strider 2: This arcade port is a bit short, but a fun side scroller regardless.