The exchanges (MtGox, BitFloor, Coinbase, etc.) are probably the closest thing to a bank currently, in that you create an account with them, transfer your money there, and then trust them to maintain control of that money for you and give it to you upon request. BitFloor is even operating in a capacity that is a bit like Fractional Reserve, in that the balances that some people have are higher than the amount of bitcoin that BitFloor actually has on hand. BitFloor avoids a "run" that would destroy them by marking those additional funds as "On Hold" and preventing anyone from withdrawing them until they can supply the necessary funds from their own revenue.
Yikes. Without an insurance backstop and/or a long history of responsible stewardship (plus, arguably, transparency), this bitfloor situation strikes me as pretty risky.
They were hacked and had customer's bitcoins stolen back in September. Rather than shutting down and causing everyone to permanently loose their bitcoins, the solution they chose to implement (after improving their security hopefully) was to lock all the current bitcoin balances as "On Hold". Then they apparently intend to use revenue to repay the customers over time, releasing the "On Hold" balances a bit at a time as they can afford to do so. This means that your balance at
BitFloor can be higher than the total bitcoins they currently have control over, but you know exactly how much of it is not currently available (which is a bit less than how much you had stored there at the time of the theft).
You can read all about it here:
https://bitcointalk.org/index.php?topic=105818.0EDIT: As of 2013-04-17 BitFloor has ceased all operations.
