This topic has come again in recent posts, as it does from time to time. I'm not a parent so it's a little hard for me to know how I'd react to a son who wanted to shave his head. The recent post about the 7-year-old seemed way too young to me, although in all likelihood that boy is probably sporting a buzz cut and not a razor shaved head.
I really don't think I'd have an problem at all with a 15 or 16 year old son who wanted to shave his head. It is, after all, just a haircut. I might even be willing to allow it at a slightly younger age, if the young man was mature enough to realize that hair does not grow back overnight, and if he didn't like the shaved head he would have to live with it until it grew back out -- and it could take quite a while to reach its previous length.
I really don't know what the appropriate cut-off age is, or if there even is one. Maybe these decisions just need to be made on a case by case basis. I'm interested in hearing the opinions of others, particularly those of you who are parents.