I currently have FFVII that I play on both my PSP and PS3.  I'm looking for something with a little more action and I'll probably play it on my PSP more than the PS3.  I saw Dino Crisis and remember renting it years ago and liking it but I guess not enough to beat it or buy it.  Any suggested titles would be appreciated.

Mega Man X4-6

Metal Gear Solid or Castlevania: Symphony of the Night?

the old Resident Evil titles (1-3) are great if you can get past how dated they might feel. also, go with MGS. can't you buy a PSP Castlevania game that includes SOTN? 

I used to own Soul Reaver, I don't remember if I ever beat it, but I think I did.  I remember liking it a lot.
 
MGS was also a thought. 
 
 I'm kind of played out on SOTN though.  I think I did everything you ever could do in that game.

MGS is a good bet.
 
If you're into 2D stuff, Megaman X4 or X5 are pretty good (albeit infuriating) sidescrollers.
 
Einhander is a pretty fun shmup, IIRC, but it's been a while since I've played it.

I would suggest  Metal Gear Solid as well. it still hold up fairly well and i hear it plays well on the psp.

MGS is a bit short, but It's really fun
 
Also try:
 
FF8
FF9
Grandia

I was going to suggest Team Buddies but I don't think it's on PSN. Damn that game needs a sequel.

Spyro the Dragon 
 
/thread

" the old Resident Evil titles (1-3) are great if you can get past how dated they might feel. also, go with MGS. can't you buy a PSP Castlevania game that includes SOTN?  "

Jet Moto

Tekken 2

The responses have reminded me of a lot of game I loved that I forgot about.  Thanks everyone.

Silent Hill, yo. I am also going to throw Crash Team Racing into the mix. It might not be the game you are looking for, but damn is that game the best funracer ever made, and was missed by many. 
 
Oh.
 
And Vagrant Story.

Gran Turismo 1 
MGS 
FF9

Final Fantasy IX
Vagrant Story

The Spyro the Dragons were pretty great-if you can only choose one I'd say choose 2 (as in Spyro the Dragon: Ripto's Rage). Then again, depends where you are from.

Any Crash Bandicoot game

" Final Fantasy VIII, Silent Hill, and Parasite Eve. "

Syphon filter 1 and 2 are pretty good.

I always thought the 1st 3 crash bandicoots were fun on the PS1.

Can't go wrong with the Oddworld games. Abe's Oddysse and Abe's Exodus (?) are two fantastic platformers. The graphic at the time was spectacular. The games are HARD though (especially if you go in with the intention of rescuing all Abe's friends), but kinda like Demon's Souls you die only because you made a fatal mistake and not because the game is unfair.
 One of the Oddworld games are out in PSN. I'm going to download it for the PSP tonight now.