I often hear about an urge to switch from checks, credit cards, and physical cash, to E-Cash, to prove an important number of benefits. For one, less overhead. Financial people tell me that writing a check can cost up to $2.00, which really puts some of those $0.90 or so checks into perspective.
Cash can be bulky for large purchases, which is more a problem in countries with major issues with inflation. (In the US, a million dollars would fit into a suitcase.) Cash also is easily stolen. If you lose your wallet, count on kissing all the cash in it goodbye, while a credit card or check could be canceled to limit liability.
Checks and credit cards require certain infrastructure to accept. Credit cards charge to a merchant account, which must be set up ahead of time and at a certain fee. Accepting credit cards also means that the merchant doesn't get paid the entire amount, but this loss is accepted because it means a greater volume of business. The merchant may not charge a fee for accepting a credit card, but may offer a "cash discount." Worse for the merchant, credit cards do not actually pay until the end of the month, putting the merchant at a considerable float. Checks are the most frustrating because of the possibility of "bounced" checks, in which the funds to pay it are unavailable, and so cashing the check results in no funds at all. (Paying with a defective check deliberately is a crime, a crime people have gotten away with for years.)
So, the usual solution posited is e-cash, in which a credit-card like device would transfer money, and encryption would make it difficult to steal or subvert. This would remove the need of the merchant to have an account with the credit card company, and the merchant would receive the full charge, instantly. The buyer would have the anonymity advantage of cash, would know in an instant if the transaction succeeded or failed, and if the e-cash card were lost or stolen, it could be canceled in an instant to halt liability, just like a credit card.
As a further precaution, I think that the processing should be centralized so that the seller need only have a communications system, like a telephone line, to provide a sale. I don't want this system to fail if local power fails, since that's often a critical time to be selling stuff. (Like, say, immediately after a hurricane.)