Most banks do. As long as you do not have a delinquent checking account. You might not be able to get the free account, but you should be able to get an account. If not you can always get the credit card that ask you to deposit money and build your credit up again. It works just like a debit card, and you can use any ATM to get cash, without penalty. Call the banks first if you have real bad credit, on go online to the banks website and try to apply on line.