Such a hard question.
It's not just age...or maturity. A lot of it is geography, too. Small towns it's a LOT easier to leave children alone then in cities. Same standpoint, where in the city, & what kind of housing. When I was a child we frequently lived in small towns or on base & I started staying home "alone" (aka with my younger sister), when I was 5. Small town, out in the country, meant my mum could knock on the next door neighbor's door and ask her to keep an ear out for us, and be gone for a few hours. Sometimes we'd meet up with other kids in the village. As long as we left a note, it was okay. Same token when I was 8-10 we lived on the beach in S California, and I wasn't allowed to stay home alone at ALL, because there was sooooo much foot traffic. As soon as we moved into a tightknit community again though, my siblings and myself (and all the other kids in the town), were allowed quite a bit of freedom.
For my son: I was tempted when my son was 5 to take the baby monitor with me to the gym at night (that was about 200 meters from our apartment) but never actually got up the chutzpah to do so. I knew a lot of other mums in our building who did, but I was too nervous.
I have friends in New York though (middle class), that their first graders catch the bus or subway or taxi home from school, do their homework, and then go meet up with other kids from their building. Some of my friends let their kids run down to the bodega, or to the local park, or play on the sidewalk... others they have to stay in the building. That would freak ME out, but in talking with them they look at me funny. Like I still fed MY first grader by hand. Theirs carry debit cards so they can hop in a cab.
The converse to your question, too, is how long do you let your children play outside alone, and how far can they go? I had to check in at mealtimes, but as long as i was there for breakfast, lunch, & dinner, I could go anywhere I wanted from the age of 10 on. My sister had the same freedom @ 8, but we were back in a small town again.
Now we have a house, but we live on a busy street near the U, so it's highly unlikely that I'd let my son stay home alone for any period of time for quite some time. As to WHEN I'd let him stay alone... Honestly, I have no idea. I DO know that I certainly had a lot more freedom then he does. I don't even let him play in our backyard alone. If I don't have any work to do out there, I grab a book or play with him.
I'll be really interested to follow this thread, to see what others do here in THIS city.
:)