Two or 3 years ago my 15yo son wanted to bleach the tips of his dark brown hair and I let him do it. It was the popular thing to do at the time and looked good in his hair.
This last summer he asked to bleach his hair again and I told him he could before finding out the details. This time he meant all over, though, which is what he did. I think it looked pretty stupid, especially at first and since he did it himself (at least it was cheap since he did it), but it grew out fast and once it started to grow out and wasn't all over it didn't look so bad and I didn't mind it too much.
The good thing about boys, assuming they have reasonably short hair is that it does grow out quickly and if they get tired of it they can just get a buzz cut and it's gone.
I've let my DD highlight (do it yourself), but her hair is naturally highlighted--the one good thing she got from me, so really there is no need for it. I'd have a problem if she wanted to dye it some strange color and wouldn't have allowed it when she was younger, but she's 18yo, so all bets are off (but her hair is beautiful naturally highlighted strawberry-blonde, so hopefully she won't).
I would not let children dye their hair, though, unless it's washout color.