A friend of mine says, "cash will always be around as long as there are politicians to bribe."
However, I've run into businesses that don't take cash. Feral Express drivers don't, nor does the local Feral Express terminal. The local State Farm office does, but they had to send someone out to the bank to make $15 in change when I paid my policy. And, famously, the US Internal Revenue Service doesn't take cash. Neither does ITAR, by the way.
Actually, ITAR goes the extra mile - they not only don't accept cash, they don't accept the US Postal Service either. Any documents you send to them have to go by private courier.