Is it possible to have a modern economy without a central bank? Many mainstream economists say that such thing is impossible. Is there some specific reason why the financial system needs a central bank?

In this video http://m.youtube.com/watch?v=BcuAOdXD0Go, Krugman says at 03:00 it's impossible to leave the central bank out of the equation today. Why is this?
It surely is possible: For a long while, Gold was the basis for the value of money in many "modern" countries, leaving central banks with little room for policies.