There are many Bitcoin wallets out there but none of them can be considered banks because nothing is insured from theft or security fraud.
Banks usually accept responsibility for loses pertaining to security hacks and fraud.
I think Mt. Gox could make the first bitcoin bank and have a "FDIC"-type guarentee because they are able to make money through other means such as trading fees on the market.
Eventually they'd be able to make money from merchant fees.
Of course, this isn't ANONYMOUS.
but neither is cash when you deposit into banks and make transactions.
If someone that stole bitcoins ever uses the bank or any other banks that communicate as a community, the bank can put a hold on those bitcoins and transfer them back to the original owner.
This solution is for the non-shady, don't care about anonymity, everyday money transactions.