Action/Adventure
The Last of Us: Remastered (Last gen's best action adventure game)
Tomb Raider: Definitive Edition (the runner up, alongside Uncharted 2)
Metal Gear Solid: Ground Zeroes (amazing stealth gameplay)
Open World
Grand Theft Auto V (the best of its kind to date)
The Witcher 3 (dope story and quests, great world, decent gameplay)
Metal Gear Solid V (play Ground Zeroes first. If you want more after that, cop this)
Shooter
Destiny (co-op FPS rpg)
Battlefield 4 (not much else out there in this style. Get this over Battlefront)
Other dope shyt you may like
Until Dawn (interactive horror movie style game)
Bloodborne (very hardcore, survival horror-ish RPG)
Hotline Miami 2 (awesome arcade style game)
Life is Strange (a lot of people love it, but it stars highschool students so demo it first)
Mortal Kombat X (my favorite fighter since SF4, but demo it first)