This depends a lot on how you count them. For instance the West African States covers eight countries, each has a unique letter associated with it. Czechoslovakia recently split into two countries, each having their own currency. Lots of former Soviet countries are creating their own currency. The Eastern Carribean dollar covers a lot of little independent islands.
Currently, there are around 175 separate countries issuing paper money. There have been many countries which have either disappeared or no longer issue their own money (Biafra, East Germany, Soviet Union, South Viet Nam, Greenland). Sometimes semi-independent governments issue their own paper (Scotland, Jersey, St. Pierre and Michelon).