In at least the US and Denmark we have the concept of systemically important banks. Bank that are to big to fail. These banks will, currently always be bailed out by the tax payers. So far it seems to have worked out for the benefit of the tax payers, because the governments have managed to make money on bailing out these banks.
What I however don't understand is why governments allow "to big to fail" banks to exist. The Danish government have actively encouraged people to choose bigger banks, arguing that there are to many banks in the country. It seems like what they should do is break up banks that are large enough to harm the nations economy, should they fail.