I could, but I couldn't live with myself afterwards.

Catherine is made by Atlus and atlus never makes a bland game, tsk tsk.

Crisis Core

Final Fantasy I and Final Fantasy II

Star Ocean I and Star Ocean II

Valkyria Chronicles II

and Final Fantasy Dissidia (My fav fighting game ever)

These are must buys.

Of my collection, I STRONGLY recommend:

• Hot Shots Tennis (Even if you don't like Tennis):  Great graphics, Pokemon-Like atmosphere, tons of replayability
• Valkyria Chronicles 2: Probably the best PSP game I own.  Good for short bursts of play like any good portable game but meaty enough to feel like a console experience.
• Resistance Retribution:  Some of the highest production values you can find in a portable game. 
• Syphon Filter Dark Mirror:  Just like Resistance only not as far "out there".
• Crazy Taxi Fare Wars:  Crazy Taxi 1 & 2 on one disc (or download).  Everybody needs Crazy Taxi on at least one console.
• Gurumin: Nobody has ever heard of this game but I promise you, it's a good time.  It's a little on the girly side, though.  Still a very solid, very cheap Zelda like experience.  Look it up on youtube if you're interested.

Other games that I like include Jeanne D'Arc, Final Fantasy Tactics (not as pretty as Jeanne D'Arc but for some reason more fun),  Little Big Planet (only one player but still as much fun as the PS3 version) Metal Gear Solid Peacewalker (good for a portable--merely okay for a MGS game), and Burnout Dominator (great racing game that's a little too fast, later on).  I may be forgetting a few.  Hope I helped you.

I'm too lazy to wade through 5 pages of thread space so if people mentioned these games I apologize. 

1. Jeanne D'arc (One of the best strategy games I ever played)

2. Megaman Maverick Hunter X (Megaman X remake need I say more?)

3. Gurumin (A gem of a game, old school PSX like game that's amazing, though childish)

4. Street Fighter Alpha 3 (Street Fighter Alpha 3)

5. Metal Gear Solid: Portable Ops (Infastructure mode is decent)

6. Killzone Liberation (Very good coop game.  Good game in general)

7. Darkstalker something (All Darkstalker fighting games in one)

8. Tekken 5: Dark Ressurection (Very good port of Tekken 5)

9. God of War: Chains of Olympus (God of War PSP)

10. Capcom Collections (Both of them, arcade games are always good on the go)

11. King of Fighters Orochi Collection (King of Fighters 94-98)

12. Soul Caliber something (Soul Caliber on the PSP comes with Kratos)

13. Brave Story (Good RPG, though can't say much of the story, though I never got that far in it)

14. Outrun 2 (Good arcade racing.  Good on the go)

15. Ridge Racer PSP (Arcade racer; the first and it's a gorgeous game).

16. Lunar (Remake of the first game I believe.  Came out recently)

17. Castlevania: Dracula X (Rondo of Blood remake.  Comes with Symphony of the Night as an unlockable bonus)

18. Gran Turisimo PSP (Heard it's very stripted down, but good on the go)

19. Tekken 6 (If for some reason you don't have Tekken 6 already)

20. Resistance Liberation (A good third person shooter).

21. Tomb Raider Anniversary (If you like Tomb Raider this port is very well done and it's very good)

22. Spider-man 3 (A good port of the PS2 version, web slinging fun)

23. X-men Legends 2 (A good beatem up if you got a few friends to play with)

24. Monster Hunter all (Fun game with friends)

25. Megaman Powered Up (Megaman the first... remake)

26.  Final Fantasy Tactics: War of the Lions (Fancified Final Fantasy Tactics)

Well I'm not near my PSP collection to name you the few more stuff (No my collection isn't that big I'm just naming games off the top of my head.).

There a lot more, like sports games and such.

I am not going to force you to buy Zettai Hero Project from NIS but I hope you give it a shot.

Here's some info.

http://www.neogaf.com/forum/showthread.php?p=20270184

It hasn't been localized yet but it will be release sometim soon.

I've heard of Gurumin!

Naruto Ultimate Ninja heroes (ONLY if you like Naruto)

Thanks for more reccomendations all

@severance

I don't mind 2D ones as long as the battle system isn't frustrating in its interface and so on to play now.

@Mirson

lol  yeah I'll probably just play 3rd B'day in Light's costume

@cross-x

Aya is hot!!!! And apparently her clothes fall apart when she gets hit!!!! Need to try to die many times in that game

And I had my eyes on Phantasy Star Portable......is the story good though?

And still 10 times better than P3 plus 4.