Basically, but they call it a thin file (aka no credit history). If you don't have someone to cosign, they'll start you off with a secure card, where you pony up a couple hundred bucks and borrow against yourself until you establish good history.
In my case, it was with the bank I already had a checking account with and the credit limit was like $500. They normally start you off with a super low limit and a high interest rate.
No teenager should be given a credit card under any circumstances. That's a great way to find yourself bankrupt.
Edit: Guys are we talking about credit cards or debit cards? There's a significant difference between the two and there's a lot of people telling me they had credit cards as teenagers, which seems unthinkable to me.
Not when teens have access to finance 101 classes in high school. It was an elective in my HS and you better believe I took it. I learned how to do my taxes, balance a budget. It was great. I wish this was a hard requirement for all HS students.
But I will agree, teenagers are pretty stupid. but at least I was a knowledgeable stupid teenager.