An anecdote: at least when I was growing up, I didn't notice anyone under 18 with a debit card; most people used cash for purchases or borrowed credit cards from their parents when they wanted to go shopping on the weekend.

That said, I don't know if there are regulations here in the US concerning debit card age requirements, but from a cursory glance of a few US banks, it looks like children under 18 are allowed to get a checking account (and hence, a debit card) provided that they get a joint account with their parents. Perhaps the policy is different for teenagers who wish to separate finances from their parents for whatever reasons, but those are edge cases.