From a 911 dispatchers perspective, I really have to say a lot of women here under estimate children during emergencies! Some of my best callers have been under the age of 15 years old. And these days, people are giving their (very young!) children cell phones for emergencies anyways. I have had some very serious emergencies called in by young children, who remain more calm and collected and give me WAY better info than most adults do in the same situation. I have literally never, in my 7 years of doing this job, had a child caller that was not 100% cooperative and easy to walk through literally life-saving instructions with. One example is a 10 year old boy that I walked through CPR on his own MOTHER. She is alive today because he didn't lose his damn mind like 98% of adults do when someone stops breathing.
As for me, I do leave my son alone at home, at 7 years old only for very short periods of time. I'll go for a run sometimes, if he doesn't feel like running with me, I only go for about 15-30 minutes at a time, and 99% of the time one of us leaves our cell phone with him so he can call one of us or the police. We also have a decent alarm system, which he knows very well how to operate and press the panic button if needed. BUT, I also keep in mind that not all children are equipped these days to be left alone at home. My son knows what he can and can't do, and I trust him to not do anything dangerous. he just plays his Xbox or Nintendo handheld or watches TV and he's usually in the same exact spot when I get home.
I wouldn't leave him alone during a work shift or the sorts probably until he's 11 or 12 years old. I'm saying that just based on what kind of child he is. I think it's every parent's discretion of course, but I was left alone at a young age with my older sister who's only 3 years older than me while my mom was at work. Yes, we got into trouble, but it was nothing we couldn't handle. Accidents are going to happen whether you're there or not, children should learn from a young age about responsibility to minimize (I say minimize, because elimination is impossible no matter how sheltered or coddled kids are) hazards, accidents, and mistakes.
Edit: I HAVE to add that my son won't ever walk to/from school or be out and about while I'm not home. Another "perk" of working for public safety is that I'm paranoid about what OTHER people will do to my child, not what he will do to himself.