My PSP picks from the bunch:
Racing - NFS:MW - After my initial hesitation to get it after the frustrating NFS:R for PSP I've found my fave portable racer ever. The handling is sublime, the racing is intense and the graphics and sound-effects are first-class.
Sports - Everybodys Golf - Wacky characters with heaps of unlockable gear, awesome courses and that great engine. Tiger Woods shouldnt have stuck with their swing-engine with the PSP analogue stick, it kills the game for me.
Puzzles - Lumines. Nuff said.
Fighting - Bleach 2 - Not the best fighter in the world but flashy moves, great graphical stylings and I love the anime.
Action/Adventure - Kingdom of Paradise - Ridiculous amounts of custom combos to string together and switch between and ace graphics although the fighting can become very chi arts dependant.
Homebrew:
PSP Revolution - Dance dance fingerstyle. The app is free, the tracks are free. Quick to get into but hard to put down.
Neo CD Emu w - Metal Slug 2. Glorious arcade brilliance.
ScummVm - Sam & Max - Like a fine wine this game has aged really well and gets me drunk. Well one of those anyway.
I'm really looking forward to the next wave of shooters and puzzlers, Splinter Cell, Syphone Filter, Katamari, Extend Extra and Loco Roco.