My 11 year old son has been running for a couple of years now. To begin with, he only did a mile or so.
As he's getting older (and taller-he's one of the long, lanky variety!), his endurance is improving, and he can do 3 miles with ease. We don't let him run further than that just yet. I'm a bit wary of overdoing things with him in a period of very active bone development.
There are often fun runs associated with adult races, and Junior Fifer has a great time doing them...he came 9th out of 60 at a 1 mile 5-15 year-olds race at the weekend, his best performance so far.
Also he runs at school at this time of year, as he's in the cross country team.
Ao I'd say go for it, if your son is keen. What better way to help him develop a healthy lifestyle!