Here's what's available, and what they are:
The Playroom (on console) - playstation camera fun times
Resogun (launch ps+) - arcade style shooter
Contrast (launch ps+) - 3rd person adventure/puzzle game
Don't Starve (2014 ps+) - sandbox survival
Driveclub ps+ edition (2014 ps+) - racer
Outlast (2014 ps+) - horror
Secret Ponchos (2014 ps+) - fighter/shooter
Blacklight Retribution (launch day f2p) - 1st person shooter
DC Universe Online (launch day f2p) - MMORPG
War Thunder (launch day f2p) - Combat flight simulator
Warframe (launch day f2p) - third person shooter
Planetside 2 (launch window f2p) - massive 1st person shooter
Doki Doki Universe (launch window app) - adventure source
Deep Down (Japanese f2p, eventually other markets) - 3rd person Action/Adventure RPG
Escape Plan (Cross-buy) - puzzle
Flower (Cross-buy) - adventure
FlOw (Cross-buy) - life simulator
Sound Shape (Cross-buy) - music platformer