Well original Dungeon Siege and most Command and Conquer games are really the only ones I've played that way...
Everything else needs two hands most of the time. I can have a quick sip during straights when I play racing games (I use arrow keys for acceleration and steering, but use brakes with my left hand) and it's also possible in FSP games, which I play with mouse (free look enabled, button one attack, button two forward and wheel click open/use).
I think I play games this way, because I am super right handed, my left hand is only good for simple tasks like having a drink or pressing the button for simple actions like jump, duck, brake and so on...
Jussi