i like open world games of most sorts (currently playing The Crew, Borderlands 2, Skyrim, and Assassin's Creed) where you can wander around and explore. world-building games like SimCity or Cities Skylines (and various other management type games like Theme Hospital or Syndicate or UFO Enemy Unknown).
i mostly play online co-op games though (Space Hulk Deathwing, Payday 2, Killing Floor, various team-based games like Battlefield, Arma, et c), and puzzle games (Portal, The Room) and very difficult platformers (VVVVVV, Super Meatboy, Brutal Mario) because they don't eat as much time (spent wandering around). i used to be pretty big into action RPG's and MMORPG's (remember Dark Age of Camelot?), but not so much any more.
its hard to find co-op people to play with on the regular though, so i'm often left alone. i play grand strategy games (Stellaris, Sid Meier's Civ games, Crusader Kings) as well. i'm a shameless achievement hunter and have something stupid like 3000+ achievements with 50 games where i have all of them (example, in Civ 5 i have 175 achievements out of 286. that's every single achievement excluding some DLCs i don't have. likewise with Payday 2 where i have 452 out of 551 for mostly the same reasons on top of just finding it boring to solo all the time).
i think i play (meaning i GM near constantly) more table top RPG's like D&D or whatever far more regularly with my friends than online videogames where it's mostly acquaintances or randos.