I don't see anything wrong in principle with bitcoin banks and credit unions, in the sense of businesses that, through some kind of mechanism, pay you interest on your BTC while finding people they can loan to at (higher) interest.
But it's still getting way ahead of ourselves. Before this kind of Bitcoin bank can exist, the Bitcoin economy must be a lot more mature, to the point that both lenders and borrowers can gauge what their payments/income would be in real terms. That requires higher liquidity and lower volatility than currently exists -- and, of course, wider acceptance.
At this point, the only function of a bank that you need is to keep your money safe so that e.g. when your government inflates your currency, you can convert back out to the inflated units. But you can already "be your own bank" in that sense, without any financial intermediary, simply by following regular protocols for backing up your wallet, running a client, etc.