To those of you who are parents of young children, how do you feel about your kids riding around your neighborhood?
I'm just curious as to what other people's opinions are as my son has now really gotten into riding his bike and I want him to get into it, get used to the idea of riding, and feel like it's an important part of life. I grew up on a farm so I'm pretty sure I was allowed to ride my bike alone as soon as I was old enough to actually ride, but obviously the city presents a very different environment than empty back country roads.
I don't have good answers. Maybe I should say that I don't like my answers. My wife and I don't encourage our children to ride on their own. We permit occasional trips to visit friends. Biking to middle school (specifically, Frick) in Oakland was off limits. The car traffic is just too intense there. We live in the city, in Shadyside. I commute into downtown essentially everyday...
Growing up in the city (Lincoln/Lemington), I had free reign over about two or three blocks from pretty early on (it helped that everything within four blocks was dead end, so there was no traffic save for our neighbors). I can't recall at what age that started, though.
As for my kids now, hmmm. Our street in Morningside is reasonably busy, but I would think by the time our oldest is 8 or 10 that he cruise around the neighborhood on his own (maybe?). By riding on the sidewalk for a block, it's easy to get a network of very quiet streets. My boys spend a lot of time in a trailer, too (and hopefully a trail-a-bike this spring), so perhaps they're already learning how to ride on the street.
We also got in the habit of allowing our five year old to have a pretty long leash when he's riding on the sidewalk. He knows enough already to stop at every intersection and pay attention when passing across a driveway. I'm not ready to let him go around the neighborhood yet, but he's clearly picking up the rules of the road.
It depends a great amount on the child, moreso than the traffic or the flavor of the neighborhood. My son rarely rode around the neighborhood, but my daughter, 4 years younger, was out and about much earlier, I think due as much to athleticism and adventurousness as to what we allowed. Before she biked to and fro, she ran to and fro. They're in college and high school now.
My wife and I never set a minimum age at which they could go out. It's a small neighborhood, though, with few kids their age within traveling distance, and is set on steep grades bordered by busy streets (4-lane Perry Highway, 2-lane Perrymont Road). If my daughter could physically travel to someone's house, she went. All we demanded is that we know where she was going and when she would be back. Thumbscrews were employed if rules were broken. 
We didn't set geographical limits. Being in the suburbs, we drove them to any house outside the neighborhood. This also allowed parents to talk, at least briefly, to verify rules, pick-up times, etc. In a huge school district like North Allegheny, the kids' friends could live 12 miles away. In terms of walking/biking, the 10 kids' houses in the neighborhood pretty much decided the non-drivable limits for us.
My beef is that it isn't easy enough to get from one suburban neighborhood to the next. Walking trails (at least legal ones) are non-existent. Any trip to any school or the public library requires a car trip. Sidewalks are sparse or absent. Few adults venture out w/o a car, let alone kids.
I have no problems with letting kids get out on bikes early. The way I see it, that decision is actually made a lot earlier, when they can walk or run to a neighboring house and know how to safely cross a street.
Interesting answers and thanks to everyone who did answer.
My son is 7 now and I consider him to be incredibly mature for his age, but he just really learned to ride his bike really well this year. Before this year we'd used a trailer bike and I would take him everywhere from down Liberty through Bloomfield/the Strip to downtown traffic and we never had a problem. So his skill is there as far as riding the bike itself, I just get worried about traffic (and a little bit about him getting snatched.)
When it comes to traffic, even excellent cyclists can get hit by less-than-excellent drivers, and take a kid who's not even as high as many cars hoods and you get even less visibility. And even as smart as I think he is, the fact is that when kids get caught up in play it's in their nature to forget about the rules and push the limits a bit.
As far as him getting snatched, I think the problem there is that he's obviously the cutest kid ever, so maybe I should just ugly him up a bit. 
Thanks again for your responses.
