I have a 15-month-old daughter. I only game when she's asleep, but if she wakes up it has to interrupt anything.
This is why I hate hate hate any game which limits pausing or saving. She woke up when I was three quarters of the way through the battle up the citadel in Mass Effect (which doesn't let you save if a single enemy anywhere in the universe has ever so much as heard a rumor of your presence within ten light years), and I lost a huge amount of progress.
I want games with a one- or two-button no-waiting command to pause, save, and shut down, from anywhere in the game (yes, even the title screen, dammit), like putting a laptop into hibernate mode.