Right, well you seem to be missing most of the really good PSP titles.
God of War: Chains of Olympus
Probably the best game on the PSP, while it's a little on the short side (8-9 hours) it still really captures everything that is great about God of War, and graphically it's still the best looking game on the PSP.
Crisis Core: Final Fantasy VII
Even if you didn't play FFVII this is a really solid game on it's own. It's an action RPG and less like your general turn based JRPG fair. Think of the combat as closer to Kingdom Hearts then Final Fantasy VII, although much of the core concept is still there (in terms of materia and equipment) just implimented differently.
Jeanne d'Arc
My personal favorite RPG on the system, Level 5 did a great job with this game, the combat is some of the best strategy gameplay out there and the plot (a take on Joan of Arc) is really well done. It would be a shame for anyone to miss this game.
Wipeout Pulse
One of the best installments of the Wipeout franchise, and the absolute best racer on the PSP. It's visually beautiful (what Wipeout isn't?) and the PSP controls work (stearing with the L&R is very intuative) really well. I dumped a lot of time into this game.
Metal Gear Solid: Portable Ops
I like Metal Gear Acid, but the gameplay is a far cry from the standard of Metal Gear, Portable Ops however is just that. If you like MGS (how could anyone not like the series) then this is a must play.
Dissidia: Final Fantasy
Don't let the name misslead you, while this game has many role-playing elements, it's a fighter first and foremost. The combat is good, each character has his/her own feel and play style and the role-playing elements (leveling up stats, equipment, summons, etc) add a great amount of depth that you usually don't see in most fighters.