In no particular order, a list of games I've either personally played or heard good things about:
Shin Megami Tensei: Persona
Shin Megami Tensei: Persona 3 Portable (Only if you can't/haven't played the PS2 one)
Phantasy Star Portable
Phantasy Star Portable 2
Valkyria Chronicles II
Tales of Eternia remake (Only Released in EU/Japan, but PSP games are region free)
Tales of the World: Radiant Mythology
Breath of Fire III (Only Released in EU/Japan, but PSP games are region free)
Final Fantasy I/II Remakes
Crisis Core: Final Fantasy VII
Dissidia: Final Fantasy
Final Fantasy Tactics: War Of The Lions
Kingdom Hearts: Birth by Sleep
Jeanne d'Arc
Disgaea: Afternoon of Darkness
Disgaea 2: Dark Hero Days
Prinny: Can I Really Be the Hero?
Ys Series
Tekken 5: DR
Tekken 6
Dragonball Z: Shin Budokai
Dragonball Z Shin Budokai: Another Road
Soul Calibur: Broken Destiny
Killzone: Liberation
Resistance: Retribution
Assassins Creed Bloodlines
Metal Gear Solid: Portable Ops
Metal Gear Solid: Peace Walker
Monster Hunter series
God Of War: Chains of Olympus
God Of War: Ghost of Sparta
Grand Theft Auto: Liberty City Stories
Grand Theft Auto: Vice City Stories
Grand Theft Auto: Chinatown Wars
LittleBigPlanet
Daxter
RockBand Unplugged
WipeOut Pulse
Kenka Bancho: Badass Rumble
In addition, you can also play a large amount of PS1 games, and if you get some emulators for it, you can further expand your potential library.
Edit: +1 on Maverick Hunter X as well, dunno why I left it out, its currently on my PSP. Also, Megaman: Powered Up isn't as good, but also worth checking out.