List of working games here:
http://www.neogaf.com/forum/showthread.php?t=488789
As of this evening:
2 Xtreme
Alundra
Arc the Lad
Arc the Lad II
Arcade Hits: Shienryu
Arcade Hits: Sonic Wings Special
Breath of Fire IV
Burst Angel
Castlevania Chronicles
Castlevania: SotN
Cho Aniki
Cool Boarders
Cool Boarders 2
Cyberbots: Fullmetal Madness
Destruction Derby
Dino Crisis
Dino Crisis 2
Final Fantasy Origins
Final Fantasy IV
Final Fantasy VI
Final Fantasy VII
Final Fantasy VIII
Final Fantasy IX
Front Mission 3
Gex 3
GaiaSeed
Hot Shots Golf 2
International Track and Field
Jet Moto
Jet Moto 2
Jumping Flash!
Jumping Flash! 2
Klonoa
Legacy of Kain: Soul Reaver
Legend of Dragoon
MediEval
Mega Man
Mega Man 2
Mega Man 3
Mega Man 4
Metal Gear Solid
Money Idol Exchanger
Pandemonium
Parasite Eve
Parasite Eve 2
Rally Cross
Resident Evil: DC
Resident Evil 2
Resident Evil 3: Nemesis
Ridge Racer 4
Saiyuki: Journey West
Silent Hill
Street Fighter Alpha 1
Suikoden
Syphon Filter
Syphon Filter 3
Threads of Fate
Tomb Raider
Toy Story 2
Twisted Metal 2
Unjammer Lammy
Vagrant Story
Warhawk
Wild Arms
Wild Arms 2
Wipeout
Xenogears
Bolded entries are ones you can access directly from the PS Store on the Vita. The rest must be downloaded onto a PS3 and then copied over from the Vita (just don't delete the "bubble" on the PS3 before copying).
Currently Incompatible Via Transfer or Direct Download:
Chrono Cross
Crash Bandicoot
Crash Bandicoot 2: Cortex Strikes Back
Crash Bandicoot: Warped
Crash Team Racing
Spyro The Dragon
Spyro 2: Ripto's Rage
Spyro: Year of the Dragon
Theme Hospital
Tomba!