There have been a number of recent stories about mass thefts of credit card data, most notably one at Target
that may have involved more than a hundred million customers. An obvious response for customers is to pay with cash, but that is inconvenient for large purchases and unworkable online.
A better solution, especially for online purchases, would be some form of ecash, some digital equivalent of currency. The only such currently available is Bitcoin, which is not yet widely accepted by merchants, although that may change—Overstock.com recently announced that it would accept bitcoins. It is not an anonymous currency—I have described it, I think correctly, as the least anonymous currency ever invented—although there are mechanisms that have been proposed to change that. But if your worry is not that other people will know what you are buying but that they will get access to your credit or bank account, Bitcoin looks like a workable solution.
An alternative, already well established, is Paypal. That does not entirely solve the problem, since Paypal itself has your credit information, but using Paypal for your payments means relying on the security precautions of one firm rather than every firm you deal with.
A better solution would be an anonymous digital currency along the lines proposed many years ago by David Chaum, ideally one denominated in dollars—the market value of bitcoins fluctuates widely, which some users would find inconvenient. The disadvantage of that mechanism, in contrast to Bitcoin, is that it require an issuer, a bank that users of the money are willing to trust to redeem it. That probably means a bank in a reasonably stable first world country. The governments of such countries are not eager to permit a form of currency that would make money laundering laws unenforceable.
But perhaps, if enough people get sufficiently worried about having their credit information stolen, there will be enough political pressure to get some country to either issue its own ecash or allow a bank to do so under its jurisdiction. Alternatively, perhaps some government strapped for cash will decide that issuing the world's first anonymous ecash looks like a good solution to the problem of raising revenue without raising taxes.
It does, of course, have to be a government that people elsewhere will trust not to take the money and run.