Mostly just one singleplayer game at a time. It depends on the scale/genre really. I sometimes mix playing one open world game and a more linear shooter for instance, depending on the mood. Right now I'm still chipping away at The Witcher 3, so still many hours to go (haven't finished main story yet).
Multiplayer is a totally different approach however, depending on the friends I have online to play with. I currently play FIFA, Rocket League, The Division, Halo 5, Awesomenauts, Destiny, Overwatch, Titanfall 2 and Gears of War 4 with friends, or Hearthstone and Elder Scrolls: Legends when I want to decompress. Player of many, master of none I guess.