I probably play emulators more than PSP games
PSP Dungeons - Homebrew FPS game that you can create your own maps/textures for. This is probably my favorite original homebrew game.
Doom PSP - Port of doom to psp
MMSPlus - Master system emulator
DGen - Megadrive (genesis) emulator
NesterJ - NES emulator
SNES9x_TYL - SNES emulator
gpPSP - GBA emulator
RIN - Gameboy/Gameboy color emulator
NEOGEO CDZ - NEO-GEO CD emulator
PSPBeeB - BBC model B computer emulator
All can be downloaded from psp-news.dcemu.co.uk and probably pspupdates.qj.net also.