Mostly single-player first-person shooters, but sometimes I play something in the 4X genre - explore, exploit, expand, exterminate (the opposition). Of the latter, one can mention Sword of the Stars and Civilization: Beyond Earth.
I'm still working my way through another iteration of Skyrim, which to me is one of the the most incredibly crafted games I have ever played. But I also enjoyed the other "Elder Scrolls" games such as Morrowind and Oblivion. I also play The Witcher and its follow-ons. I'll play the cheapies as well as the more complex games. Fallout is a lot of fun if a bit grim sometimes. Half-Life is enjoyable. In the past I've played (hold onto your hats) Doom (I, II, and III), Quake (I, II, and IV), Hexen (I and II), The Heretic (A Doom variant), Sin (I & II), Mech Warrior (II, III, and IV), Titan Quest (I & II), Diablo (I & II), Dungeon Siege (I & II), Wing Commander (I, II, and III), Wolfenstein (Another Doom variant) (I & III), and a few more for which the titles escape me at the moment.