Unlike the Xbox One, the PlayStation 4 will play host to a whole lot of free games, many of which will be available through the PlayStation Plus service. Though not exactly free, you'll need to pay for PS Plus you want to play multiplayer games anyway, so you'll be doing that, pretty much.
In addition to these "not actually free, but we're calling them free anyway" games, the PS4 also has a whole bunch of free-to-play titles that are available without PS Plus.
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
Keep in mind that some of these games are cross-buy, meaning that you'll have to own them first on the PS Vita if you want to get them for free on the PS4, and vice versa.
