Kids up to about age 11 should ride on the sidewalk and, as such, should be allowed to ride on the sidewalk. Beyond that, they're better off on the street. The final call is with the parents.
The other day I was out riding and came to a place where the bike path crossed a road using a cross walk. There was a father and daughter(about 11 years old I'd say) at the crosswalk. The father was instructing her how to ride safely, and told her it's best to walk across crosswalks. I liked how the father was taking the time to teach his daughter safety skills. I was actually tempted to get off my bike and walk across when the time came to set a good example. However, the father may have sensed that he should say something because I was there and he knew I would probably ride across. So he told her that when you get older and more experienced it's ok to ride across. In doing so he let me off the hook, but otherwise I would have walked. It's nice to see people spending time with their kids and teaching them about life.