I don't have that new fangled Xbox-1 or whatever those astronauts call it, but for the 360 I liked Fallout: New Vegas (post apocalypse game), Tenchu Z (ninja game), Red Dead Redemption (western game), GTA 4 (Kstatida game), Way of the Samurai 3 (ronin game), and Dragon's Dogma (perma game). There's also some new indie game called Skyrim, it's pretty good. Only Red Dead and Tenchu Z have any sort of multi-player, but single player is much more involved. Dragon's Dogma has an option where you play single player and it calls it multi-player.