Well, I'm pretty open to most games outside of bro games (IE Call of Duty, Modern Warfare, you get the idea), simulation, and sports games.
On my PS4 I have:
*Injustice: Gods Among Us
*Minecraft
*Dragon Age Inquisition
*Tomb Raider Definitive Edition
*The Last of Us Remastered
*Lego Marvel Superheroes
*DC Universe
as far as multiplayer games go, and on my PS3 I have:
*Doom Classic Complete and Doom 3 BFG
*Diablo III
*Katamari Forever
*Sonic Adventure II Battle
*Bioshock 2 and Infinite (which I can't remember if it has multiplayer modes or not)
*Tomb Raider (came with PS+)
*Dragon Age Inquisition (had it on here before I decided on a PS4)
as far as multiplayer goes.
As far as non multiplayer, I have the entire God of War, Ratchet and Clank, Mass Effect, Sly Cooper, Kingdom Hearts, and Jak and Daxter collections, Tales of Xillia 1 and 2 and Graces F, all of the Infamous games and DLC, and a good number of other games in practically ever category save for ones mentioned in the beginning.