The idea of cash transactions is something that we take for granted in the real world. With cash, we can purchase goods with complete anonymity, in that the store clerk can observe physical appearances, but knows nothing of more personal information. Cash has many qualities, such as its inability to be linked to an owner and its portability, that we would like an electronic payment system to emulate. But there are a lot of problems inherent in the electronic world, such as the ease by which things are duplicated, which makes deploying an digital cash system difficult.
The general paradigm for digital cash involves the use of tokens or "coins". Basically, what happens is that the user's computer generates a serial number for the coin and sends it to the bank. The bank notes the serial number, puts the coin in an envelope and sends it back with a digital signature. Then the user can send it to any merchant to purchase a product. The merchant gives the coin back to the bank. The bank checks to see that the coin has only been used once, and then pays the merchant, who then sends the user the product. Since the vendor receives a coin that cannot be linked to the user, even through the digital cash company itself (since the serial number was generated by the user and then encoded), anonymity is protected. See Digicash's method, and also an Interview with David Chaum, founder of DigiCash.
So why haven't these digital cash companies been able to create a product that is marketable? CyberCash's CyberCoin has been discontinued. DigiCash went bankrupt in the United States. First Virtual Holdings, an online bank, disappeared. AtGuard, maker of privacy software, was sold to Symantec, a large company that could afford the loss if AtGuard floundered (and thus, was relatively unconcerned and unaffected when that happened). Why did these companies, and thousands of other similar companies, fail?
As it turns out, the complexities inherent in a digital cash system, combined with the acceptance and ease of use of the current system, make marketing a successful implementation extremely difficult. But, there's still hope that some company will find the edge necessary to make an anonymous system of payment feasible.