A Technocrat's Wet Dream
The idea of a cashless society has been knocking around for a while. It's a technocrat's wet dream.
As others have said, if every transaction is recorded, it's taxable. That's just one element. There are serious papers doing the rounds that from a Central Bank's point of view they can then completely control the money supply, the rate of inflation and best of all (from their point of view) the interest rates.
If all money is electronic then the concept of negative interest rates become a reality that affects every individual directly. Consider if the BofE decides on a negative interest of -5% applied to all money holdings !
Cash will never die. The definition of what cash is may change, but the designation of something to be used as a means of exchange will always be with us. 70 years ago much of Europe used the cigarette as a form of money. Communities and individuals exchange labour or goods to mutual benefit without it being recorded.
There will be an interesting fight between those who want to use technology to control and monitor every transaction and those trying to create anonymous eco-systems of electronic cash. My bet is that the crypto-currencies will end up being subsumed, if not slaughtered.