jeanne arc for sure as someone mentioned earlier
Umm the star ocean games are not bad at all. Combat feels old but still great classics!
you could download final fantasy 7 to your psp which is what i did.

Final fantasy tactics is also great!

Phantasy Star Portable

Best PSP game i've played yet, its a Action JRPG with charmingly good graphics and a great dungeon style vibe of a battle system and farming.

I've played quite a few PSP games up till now, now that i think about it, and this one is at the top IMO... i enjoyed/enjoying more then GoW Chains AND Crisis Core...

Theres just so much gameplay!

I just got Valhala Knights and Puzzle Quest recently (Val today lulz) and so far PQ is AMAZINGLY ADDICTIVE CRACK of a Portable game, while Valhala is... Sub Par so far... Not the best, but enough to keep you busy for an hour or 2...

And you already have MHFUnite so... and thats one of the best recent releases, Dissidia Should be really good to, but it comes out in aug... so...

I say, give Valhala a try, its only $12 - $15 @ Amazon, while Puzzle quest is only $14 !!!!!

Theres alot to choose from when it comes to PSP, so just take your time man. :D

Resistance: Retribution is a good game, if u like shooter games u probably like this one

There are a few top name games coming out latter this year and early next.

Kingdom Hearts: Birth By Sleep
Dissidia: Final Fantasy
Assassin's Creed: Bloodlines
Gran Turismo PSP

They all look reeeeally good.

Get Jeanne D'arc off the PSN Store (its hard to find a copy on UMD )

R & C Size Matters is great

GTA Chinatown Wars is coming this fall

SOCOM Fireteam Bravo 3 is coming this fall

SW Battlefront Elite Squadron is coming this fall

Just wait until Christmas, though I would recommend Pursuit Force, silly but most brilliant games, you spend much of your time jumping between vehicles

Resistance: Retribution
Killzone: Liberation
Ratchet & Clank: Size Matters
Ace Combat X: Skies of Deception