These are all games I personally enjoyed that meet your criteria off the top of my head.

Brave Story New Traveler
Initial D Street Stage
Persona 1
Armored Core Formula Front
DJ Max Series
The Legend of Heroes Trails in the Sky
Jean D'Arc
Phantasy Star 1
Killzone Liberation
Ace Combat (Skies of Liberation & Joint Assault)s

This complaint about the PSP always blows my mind, I have at least 30 titles in my current collection and I've probably played 60 during its lifetime just scratching its surface. Maybe 20 out of those were crap and the rest I enjoyed, if you can't find any worthwhile games then you really aren't looking.