Crisis Core: Final Fantasy 7
Metal Gear Solid: Peace Walker
Lumines
God of War: Chains of Olympus (Haven't played Ghost of Sparta)
If you like turn based strategy games, then Final Fantasy Tactis: War of the Lions or Jean D' Arc are excellent choices.

I took years but I finally got Crisis Core today for the PSP. First impression is very positive. I kinda wish I'd have paid full price for it.

GoW: Ghost of Sparta
GoW: Chains of the Olympus
Final Fantasy: Crisis Core
Monster Hunter Freedom Unite
Metal Gear Solid: Peace Walker

ooh you have to! its absolutely an awesome experience!

I know I should, the game looks great and everything I have read about it looks epic. About how long is it compared to Chains of Olympus?

1) The Legend of Heroes: Trails In The Sky
2) Metal Gear Solid Peace Walker
3) The 3rd Birthday (Though this one I can't unconditionally recommend. Yes, a lot of the criticism this game gets is valid). But this was the most addicting game I've played in a while. Despite not really fitting in the parasite eve universe (Except for like 5 minutes). I loved it.
4) Final Fantasy VII: Crisis Core
5) Metal Gear Solid Acid 2

Here's ones that others love more than most of the games I put, that I don't... Kingdom Hearts BBS, Final Fantasy Dissidia. Tactics Ogre as well barely missed my top 5 on  a basis of I not liking SRPG's.

much longer and more variety too

Killzone Liberation, Valkyria Chronicles 2, Gods Eater Burst (really should have kept original name God Eater Burst) which if you wanna Ad-hoc party with me, my PSN is Onikenshi, plus the DLC extra challenges is free, and I put in nearly 170 hours! We also have FF IV complete collection, God of War Ghost of Sparta (Chains of Olympus was very good also, but ghost is better), modnation racers psp version was loads of fun, the persona games, Y's games, Resistance Retribution, among several others.

hmm I dont know anymore, but I played it two times in a row in a VERY short time cuz of its variaty and greatness, so its definately longer in terms of replayability :D

It's one of my favourite Final Fantasy games and my favourite story in ANY game.

It's a perfect blend of old and new, and while it might be linear, it has an epic scale for a portable game.

Hope you enjoy the game!