The US dollar was in fact based on gold untill the 1970's when the government passed an act that changed it because gold prices were getting harder to control.
Originally the papaer gold and silver notes could be redeemed for gold and silver, although they eventually put a stop to it.
The point being, that unless a currency is based on something of value then it is worthless.
If someone walked up to you and handed you a round rock with a dot on it and told you it was worth alot, would you believe them? What is his estimation based off of? What does the rock represent to gain it's value?
I could see tribes having their own inner tribe currencies, but for the most part, trading will be done on the barter system because any type of currency will be worthless.
If you were in a wasteland and were trying to survive, wouldn't you rather have something you can use instead of just some paper that is probably more usefull as a firestarter than currency?