In the UK we have an organization called the FSCS who are meant to provide some compensation for anyone who has lost money due to wrong doing in a financial organization. I think if RBS And Lloyds had gone bust in 2008 then the FSCS would have been swamped with claims and would not have been able to pay them.
Other than that I think we would be doing ok now. If we had let them go bust, then we would not have a huge deficit and the banks would have regulated themselves without anyone having to tell them to.