I pay off my credit cards in full each and every month. :)
But seriously, if your credit card company does do this, simply write them a nice little note saying that while you will make the payments, also enclose the cards cut up, and explain that you will never do business with the bank that issued the card ever again, and that you will tell all your friends to never use their cards again.
"also enclose the cards cut up.."
I'm not so sure that's an option for the type of people likely to be paying the minimum now.
People who "pay off [their] credit cards in full each and every month" bring loss to the credit card companies. For this loss other credit card users must pay :)