I play massive amounts of Dota 2 these days, almost always with my wife, but that's all for PC games at the moment. When my desktop computer isn't screwing with me (computer suddenly stopped recognizing the SSD I use for boot and programs, after I shut it off in May and tried to turn it back on in September, go figure), I also enjoy the Civilization series (loved IV and V, still getting into VI), SimCity (but ugh, it's buggy), The Sims, and various online games like backgammon, spades, and of course poker. Overwatch is okay, but I have a hard time dealing with WASD controls in FPSs; I grew up with Quake, but most of my shooters have been on console, so I'm much more adept with a console controller.
I also recently made the switch from Xbox to PlayStation, so PS4 it is. My main slate of games are the Fallout and Elder Scrolls series, and I go on a long stretch of Assassin's Creed sometimes too. I also bounce back to FPSs once in a while, though I lost my zeal for those with Call of Duty: Advanced Warfare (c'mon with the jet-boost crap). The Modern Warfare ones were always my favorites, but they really butchered multiplayer with AW. Halo is good too, but I just haven't been into it as much lately, and of course no more of that, since it's Xbox exclusive.
Also, there's this odd game called Culdcept that's like a tabletop card game (e.g., Magic) blended with Monopoly. Last non-portable iteration was Culdcept Saga on Xbox 360, and before that Culdcept on original PS. You roll dice to move around an interactive board and place creature cards, and your opponents can either try to fight if they land on them, or concede and pay you a toll. There are item and spell cards you can use along the way. It's not the most popular game, but there's a dedicated core of followers, and even playing against the AI is pretty fun.