I'll start by saying that we live in the country and I might be a little less relaxed if we lived in a town. My children are 10 and 7 and are allowed to:
Go to the post box (5 minute walk, no roads to cross)
Go to the shop (2 minute walk, no roads to cross)
Go to the park (4 minute walk, two roads to cross) and to play there on their own for half an hour
Play in the moat and fields that back onto our house for up to two hours at a time. (They can - mostly - be seen from the house.)
They have been allowed to do all this for the past 18 months since we moved here. We had some friends round recently whose children are older (12 & 13), and were horrified when I told DD1 and DD2 to take them into the fields and show them their "camp" they had made. These children are not allowed out of the parents' sight - we walked down to the river and one lagged behind and the mother went hysterical when she realised she couldn't see her DD (who is 13).
Surely unless we allow them a small amount of independence they will have difficulties adjusting to "real life" as they get older?