The Federal Reserve Bank of Boston has released a Discussion Paper - Who Gains and Who Loses from Credit Card Payments? Theory and Calibrations.
Here's the abstract:

What does this mean? Well, in a nutshell, if like me you pay for a good with cash, you are subsidizing all those folks who pay by credit card and who benefit from card rewards programs. This is because the card companies charge merchants 1-2% of the price of a product when a customer uses their credit card. The merchant then raises her prices to compensate for those charges, yet if you pay by cash you don't get to pay less - which would be the true cost of the item; i.e., minus the card company charges. Apparently the credit card companies make the merchants do this. Therefore we cash payers are subsidizing credit card users.
It also gets a bit complicated as [the mysteriously named] Economist blogger M.S. posted:
The Boston Fed paper argues that cash users lose from bundling, while credit-card users win. But an alternative view would be that both lose, since credit-card users lose the opportunity to save money by using cash. For example, on a recent purchase of airline tickets in an emerging-market country, I saved about $200 by paying cash rather than using a credit card. In America, I wouldn't have been able to do that. Using the credit card would have been "free".
I'm sticking to cash. Meanwhile American Express is offering select customers $300 if they pay off and close their credit card accounts. It's not a gift really, they are worried that people will default on their loans.