I've been playing Blacklight Retribution. Loads of fun.
Planetside 2 also looks quite interesting, but it has a steep learning curve and I abandoned it.
Star Trek Online is free on PS4, which is cool!
Ingress. But it's not a game. It's like the Matrix - you can't be told what Ingress is, you have to experience it for yourself.
Keep calm and Enlighten the world!
Would you really want to though? My 360 was hacked and I wished I hadn't hacked it. Second hand games for the PS4 are cheap af. I wouldn't hack my PS4 even if I could.
Shinobi on arcade. Still, after all these years.
Also, Metal Gear Solid (the one on PS1), Ocarina of Time and Red Dead Redemption. On the PS4... probably Assassin's Creed Syndicate.