I believe we are witnessing the breakdown of the global financial and monetary system, and that at some point in the process, paper money could become worthless. However, I also anticipate the possibility that there could be a period or periods during which the credit and banking system has broken down, but people are still accepting cash that has not yet hyperinflated or otherwise become worthless. Others have already mentioned disaster experiences that fall short of complete breakdown, but during which the system didn't function. All of this speaks to the desirability of having some ready cash in small denominations to get you through at least a short-term crisis. How much you would keep in a bugout bag, or in some other way out of the banking system but still readily accessible, depends on your circumstances, but I think it should be as much as you are comfortable risking the loss or theft of. In a bugout bag, a couple/few hundred would not be too much.
EDIT: And Jarhead's thought of having some real silver is an excellent idea.