What is the youngest age you can be to open up a bank account???
In most states you have to be 18, because under 18's do not have the ability to enter into legal contracts. Some states differ, and some states allow deposit-only type of accounts. Ask at the bank.
If you can't open an account under your own name, many banks do allow you to open a JOINT account with another person who is over 18 - like a parent.
Also consider credit unions, as their rules may be more flexible.
Good Luck!!