If you don't own a PS3 or a PSP then there's going to be a lot of new content on the Vita for you. A lot of PS3 multiplats or portable spin-offs of PS3 franchises will be completely fresh to you.
I recommend:
PSV
- Persona 4 Golden (Best game on the system and one of my favourite games of all time. Significantly more charming than the PS2 version.)
- LittleBigPlanet Vita (Similar to PS3 version, but it'll be fresh to you.)
- Gravity Rush
- WipEout 2048 (Best portable racer.)
- Uncharted: Golden Abyss (Best portable TPS.)
- Dragon's Crown (Also on PS3, haven't played it but reviews are good.)
- Rayman Origins (Multiplatform, but I always felt it fits portables better.)
- Mortal Kombat
- Zero Escape: Virtue's Last Reward
- Metal Gear Solid HD Collection
- Ragnarok Odyssey ACE (Upcoming.)
- Rayman Legends (Upcoming.)
- Ys: Memories of Celceta (Upcoming.)
- Killzone: Mercenary (Upcoming. Even if you aren't into FPS, give it a try. It'll be the definitive FPS and multiplayer experience on portables.)
PSN
- Limbo
- Guacamelee!
- Jet Set Radio
PSP
- GTA: Liberty City Stories
- GTA: Vice City Stories
- God of War: Ghost of Sparta
- God of War: Chains of Olympus
- SMT: Persona
- SMT: Persona 2 Innocent Sin
- SMT: Persona 3 Portable
- Metal Gear Solid: Portable Ops +
- Metal Gear Solid: Peace Walker
PSOne Classics
- Crash Bandicoot 1/2/3/Racing
- Resident Evil 1/2/3
- Spyro 1/2/3
- Metal Gear Solid
- Tomb Raider 1/2/3/4/5
- Silent Hill
- Pandemonium
- Dino Crisis 1/2 (Not in EU
.)
- Xenogears (Not in EU either.
- Vagrant Story
- Toy Story 2
- Chrono Trigger (Not in EU.)
- The Legend of Dragoon (FUCK YOU SCEE)
Final Fantasy!!!!!
PSV
- Final Fantasy X HD
- Final Fantasy X-2 HD
PSP
- Final Fantasy I
- Final Fantasy II
- Final Fantasy III
- Final Fantasy IV
PSOne Classics
- Final Fantasy V
- Final Fantasy VI
- Final Fantasy VII
- Final Fantasy VIII
- Final Fantasy IX
- Final Fantasy Tactics