You can play these PS3 games with DualShock 4 -- PlayStation Universe

PS1 Games
Call of Duty: Modern Warfare 2
Call of Duty: Modern Warfare 3
Call of Duty: Black Ops
Call of Duty: Black Ops 2
Castle Crashers
Portal 2
Far Cry 2
The Last of Us
LittleBigPlanet
LittleBigPlanet 2
Ni No Kuni: Wrath of the White Witch
Heavy Rain
Uncharted: Drake's Fortune
Uncharted 2: Among Thieves
Uncharted 3: Drake's Deception
Red Dead Redemption
inFAMOUS
inFAMOUS 2
Resistance 2 (needs a DualShock 3 to get past the start screen)
Killzone 3
Dead Space
Battlefield: Bad Company 2
MotorStorm: Pacific Rift
MotorStorm: Apocalypse
Tomb Raider
Prototype
Skyrim
Dark Souls
Battlefield 3
Far Cry 3: Blood Dragon
Final Fantasy XIV: A Realm Reborn
Super Stardust HD
Diablo III
BioShock Infinite
Kingdom Hearts HD 1.5 ReMIX

And, games that are confirmed to NOT work:

Grand Theft Auto V
Resistance 3
Jak and Daxter HD Collection (only the analog sticks work)
Gran Turismo 5