I think I might buy one!
PS1 Games
Call of Duty (MW2, MW3, Black Ops, 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 (no motion sensing)
Uncharted 1/2/3
Red Dead Redemption
Infamous + Infamous 2
Resistance 2 (had to use a DS3 to get past the start screen, but DS4 worked fine after that)
Killzone 3
Dead Space
Battlefield: Bad Company 2
Motorstorm (Apocalypse, Pacific Rift)
Tomb Raider
Prototype
Skyrim
Dark Souls
Battlefield 3
Far Cry 3: Blood Dragon
Final Fantasy XIV
Super Stardust HD
Diablo 3
Bioshock: Infinite
Kingdom Hearts 1.5 HD
The PS5 Exists.