Kids today do less and less of their shopping at malls and more and more of it online. I know ours do - -they buy songs off iTunes and order clothes off websites and download movies online and otherwise have little need for cash and a lot of need for a credit card.
Instead of giving them our maxed-out credit cards, I've gone and gotten them a Prepaid Card from Netspend. Netspend lets you get reloadable prepaid debit cards that work like any other debit card but without having a bank account or credit check. It's helpful not just for people who don't want (or can't qualify for) traditional bank accounts, but in our case, teens who don't want us to give them cash to buy the stuff they need - -they want to shop online, so we can pay an allowance to them on the Netspend card and they can use it where, and when, they like.