I recently picked up a used Vita so I'm looking for game recommendations.

I'm partial to RPGs but am open to other genres as well.

Thank you in advance for the recommendations.

final fantasy 6 7 8 and 9
corpse party is also worth looking in to

ridge racer type 4 as well

If you haven't played any PS1 games so far, check out the following list (i don't list any sequels but make sure you don't miss them wherever applicable):

Bold = No Brainer (i don't use bold on RPGs though - i guess you'll play them all)

Castlevania: Symphony of the Night
Metal Gear Solid
Oddworld: Abe's Oddysse & Exodus
Crash Bandicoot
Alien Trilogy
Disruptor
In the Hunt
Resident Evil
Silent Hill
Rayman
40 Winks
Ace Combat
Chrono Cross
Chrono Trigger
Agent Armstrong
Grandia
Alundra
Armorer Core
Breath of Fire
Bust-A-Move 2
Colin McRae Rally
Colony Wars
MediEvil
Die Hard Trilogy
Gran Turismo
Dino Crisis
Fear Effect
Powerslave
Vandal Hearts
Final Fantasy Tactics
Gauntlet Legends
Heart of Darkness
Hexen
Legend of Mana
Mortal Kombat Trilogy
Tomb Raider

There are many others that i can't remember of course...

As for PSP games:
Echochrome
Daxter
Crush
Jeanne D' Arc
Exit
LocoRoco
Ratchet & Clank
Patapon
Tekken Dark Resurrection
Silent Hill Origins

No idea about the Vita, but The Legend of Dragoon is a criminally overlooked PS1 RPG.

Suikoden 1 &2 are must played games. It's my personal gold standard of jrpg.
Serious storyof a rebel group taking out ambitious and cruel ruler told in a lighthearted way. Beautiful sprite, interesting character interaction, good storyline that's not about saving the world, turn base battle system with ability to combine magic, this game is a rare experience.

Vagrant Story
Parasite Eve 1 and 2
Final Fantasy Tactics
Tactics Ogre
Hoshigami: Ruining Blue Earth
Final Fantasy 7 and 8
Legend of Dragoon

I would anti-recommend FF7: It's a horrible game.

On the other hand, FF5 is really good, but I don't know how the PS1 version plays on the PSP. (That version, which is probably the worst (non-smartphone) version of the game (they messed up the audio), had a problem that would corrupt the display when trying to save on a PS2, and apparently would even crash on a PS3.)

FF4 is also good; the PSX version is, of all the official English versions, the closest to the original version in terms of gameplay, difficulty, and game balance. Again, I would anti-recommend FF7. (I haven't played FF8 except the PC demo, but it seems to have many of the same problems.)

Great fighting game with RPG elements:
- Dissidia Final Fantasy (also has sequel, Dissidia Duodecim)
Dungeon Crawlers:
- Class of Heroes II (avoid the first game)
- Unchained Blades
- Elminage Original
Action/RPG:
- Lord of Arcana
Tactics/RPG:
- Spectral Souls
- Blazing Souls Accelate

"Brave Story New Traveler" is supposedly good, but I never played that one.

Those, which I listed are pretty much PSP exclusives.

There also should be some Disgaea ports (if you are into light-hearted Tactical RPGs) and Persona ports (if you are into some rather disturbing and punishing RPGs).

PS1 also has two Lunar Games (Silver Star Story and Eternal Blue) - both are great RPGs. Also Dragon Warrior VII, which is probably the longest jRPG.

What's wrong with the first game?

(Note that I don't actually have a device that can play it, so I won't be playing it any time soon; I'm just curious.)

How do you get the cd from ps1/2 into the memory card.slot?

It was bad in every way possible. It was lagging and freezing every so often. Bosses had super-random HP - you could one-hit kill them or, if you were unlucky, hopelessly die. Maps were random, but they had only few templates and were mirrored unto themselves, and soon you were visiting repeated maps.

Class of Heroes II doesn't have any of those problems (and no random maps, all maps are handcrafted) and is actually a very good game.

Were you an expensive child to raise? ;)

You can buy the games digitally and play them on any Sony console.

Ys Seven.

I would have also recommended the first Blood Omen, but unfortunately, the American version isn't compatible with the Vita yet.

Don't know, I was too young to do the accounts.

So there is emulation for ps1/2 available then? I thought Sony had said there was only limited support for certain games on ps3? Are the games you buy from the store drm free? I mean can you save to memory card and use on other devices and such like?