Re: How old before you let your child........ and why?
Honestly, it really just would depend on the specific circumstances of the specific situation. My oldest was going to our neighborhood playground when she was 6, by herself. However, it was less than a 3 minute walk, and I am in one of those developer designed subdivisions with a park in the middle and only 2 ways in and out. And to get to the closest way out from the playground you had to go past my house. Although I could see the playground from my yard, there was a house or two behind us that blocked part of the view at times. But again, it wasn't a super appealing place for someone to pick kids up. It is in the "common area" of the neighborhood, and at least 10 to 20 homes have a perfectly clear view it. In addition, while there are kids that play there regularly, it's not a SUPER BUSY playground...it's not someplace where an adult to hide in the crowd. And, it's not a public park, it's private to our neighborhood. That doesn't mean there's like a gate and someone checking addresses or anything, just that it's not something people generally come to from anywhere outside the neighborhood. Overall, it's just a REALLY low risk situation...my kid was more likely to hurt herself by falling or crashing her bike on the way, than she was in danger from anyone else.
However, change the situation to a public park, very popular, large and near major roads, and that isn't something I would let a 6 yr old or younger do alone. It's all about the situation and the individual risk of the situation, there is no generic age or rule that I hold.