FF7 Crisis core is my favorite game ever. The gameplay, story, voice acting and music are all top notch.
DEF Jam Fight for NY is another PSP favorite for me. I really liked the combat and customization options for your character. It was just an enormous fun game.
Daxter was the first PSP game I played and it was also just an really fun and good game.
Dissidia Final Fantasy is als just a really good game with an amazing combat system.
The naruto games were really good. I think it was the ultimate ninja heroes games that had this interesting gameplay and also a story mechanic with an floor system that you had to climb and play through.
Bleach heat the soul series are fun fighting games. I think not all of them were released in the west but I recommend them because the gameplay was super fun.