Here is my list of my favorite Playstation Vita games (I don't own everyone in this list and I am not including PS1, PSP and Indie games). :)
Minecraft
Tearaway
Killzone: Mercenary
Uncharted: Golden Abyss
Soul Sacrifice (most underrated game on PS Vita imo)
Need for Speed: Most Wanted
Gravity Rush
Persona 4: Golden
Final Fantasy X / X2 HD Remaster
God Eater: Resurrection
God Eater 2: Rage Burst
LittleBigPlanet Vita
Freedom Wars
One Piece: Burning Blood
Assassin's Creed 3: Liberation
Zero Escape: Virtue's Last Reward
Zero Escape: Zero Time Dilemma
Street Fighter x Tekken
Borderlands 2
Dragonball: Battle of Z
Mortal Kombat
Ys: Memories of Celceta
Injustice: God's Among Us
Rayman Origins
Rayman Legends
Toukiden: The Age of Demon's
Toukiden 2
Tales of Hearts
Wipeout 2048
DanganRonpa
DanganRonpa 2
DanganRonpa: Another Episode
Sly Cooper: Thieve's in Time
Sword Art Online: Hollow Fragment
Sword Art Online: Lost Song
God of War Collection
Ratchet & Clank Collection
Jak & Daxter Collection
Sly Cooper Collection
Metal Gear Collection
The Legend of Heroes: Trails of Cold Steel
The Legend of Heroes: Trails of Cold Steel 2