Seeing how I live in Japan, I have easy access to these "imports" you all speak of.
BUT, as I'm just getting into the homebrew scene, I haven't played anything newer than Talkman as I don't want to update my firmware just yet.
Anywho, here's my list:
Guilty Gear XX# Reload - My favorite fighting series, and its pretty decent on PSP, but I can't understand why the graphics took such a hit. Still plays very well.
Brain Trainer - I'm waiting for the US versions of the DS ones so I can't really compare them, but it has some fun math/logic puzzles. Easy menus and such too.
Taiko no Tatsujin - Best PSP game I own. Its just SO much fun and the song list is great (if you like more recent Japanese/video game music). HIGHLY recommended.
Space Invaders Galaxy Beat - $12 off Play Asia, sounded great in descriptions, kinda sucks.
Talkman - I was so excited to get this at first but I played it once and haven't taken it out of the box again since. It just feels like a touristy gimmick more than a true speech translator. For what it does, it does well however (mostly basic phrases and stuff I already knew)