> Except when you're sleeping?
24/7 is by definition when you're sleeping. As in "call me when I'm asleep, and I'll get up and take care of your emergency".
But I always have a 3G-enabled phone near me and I always keep a laptop around. I also have monitoring in place that alerts me in case shit happens before my managers even notice.
This is not about being available 24/7, but about being available when needed. That's in case of emergencies, which by definition are exceptional.
Also, if your customers are suffering because of a problem, good customer service means waking up and fixing the problem at 00:00, regardless of your location.