I began leaving my older kids when they were young 9 and 7 year olds for very short, close-by errands. When I first started, I had very strict rules about what they could do while I was gone. Basically, they could only sit and watch tv or play video games.

No eating, no physical activity that could possibly result in harm, etc. As time went on and they and I got more comfortable, I started easing up the restrictions and allowing a little more time and distance. I always have my cell phone and they could also reach their father at work if I didn't come home for some reason. Now they are 10 and 8, so it's been about a year since we started leaving them alone. I'm still uncomfortable if I'm going to be more than about 15 minutes away, and I still don't allow cooking, eating highly choke-able food (like popcorn or hotdogs), outside play or rambunctious play, but I'll let them stay up to 45 minutes and do other low-energy activities if I'm not far away. There have been a couple of occasions where we've left the 10 year old by herself for a longer distance, but only when she agrees to be in her room reading the whole time.
My biggest concern is what someone else said about being able to handle the worst case scenario. I feel pretty confident they could get themselves out of the house in case of fire, or call 911 in a medical emergency, but I never leave the almost 3 year old with them, even if he is sleeping, because I don't want them to have to worry about what to do with him in case of an emergency. Right now I'm thinking that when they are 12, 10 and 5, I'll start to be comfortable leaving all 3 of them together for short times. I will love that day when it comes!
