Most of the time I focus all of my attention to a game. I enjoy putting everything else aside for an hour or two in the evening and just losing myself in a game. But I also just like to be focused on one thing at a time anyway. That way I feel I've got the most out of whatever it was I was doing.
Occasionally if I'm grinding on an RPG like Pokemon and not going for any story sections I'll listen to some music, or be glancing up at the TV or something. B-Spec mode on Gran Turismo always struck me as boring and slightly pointless until I figured out I could have it on earning credits without my attention just long enough to let me get some decent studying/ essay writing done.
But 90% of the time, complete focus, headphones on, world cut off.