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.