Planet Coaster - it's similar to Rollercoaster Tycoon, and basically the most modern theme park tycoon you can get right now.
Cities: Skylines - instead of a theme park, it's a city. Like SimCity, but better.
Brutal Legend - it's a "metal" game starring Jack Black. It's just fun to play.
Borderlands - this is basically one of my all-time favs, though if you're going to get into the game for the first time, Borderlands 2 is a solid starting point. The base game is great, but it's definitely better with the DLC.
Stardew Valley - this isn't for everyone, admittedly. It's relaxing, slow, and full of RPG goodness.
Just Cause 3 - someone else on here already recommended Just Cause 2, which is still a great game. However, JC3 is simply bigger. It's a direct upgrade to JC2 in almost every single way. Think of it as GTA, but where your primary objective isn't robbing banks, it's blowing shit up.
Saints Row 2 - this is by far the most comparable game to classic GTA, and the best in the Saints Row series. Controls are dated, and driving mechanics aren't super fluid, but it's still an all around great game.
Saints Row 3 or 4 - unlike the first two games, Saints 3 and 4 take a far more silly approach, and just focuses on mindless fun. It's very silly, stupid, mindless, and absurd, but it's also a fun game, and one that I really enjoy.
LA Noire - if you're looking for a pure story game with you being a detective in 1940's LA, then LA Noire is really the best thing you can get. I own multiple copies of this (alongside other Rockstar games) and really can't recommend it enough. However, it's not for everyone. You're a detective, and sometimes being a detective is slow.
Deus Ex: Human Revolution - this is a fantastic story driven game, and a pretty iconic one at that.
Doom - it's just mindless shooting. Super fun.
Mirror's Edge - a modern classic as far as I'm concerned. It's mostly based on movement, and going through levels as fast as you can. Highly stylized, with combat being entirely optional.