The 2012 edition of Bain & Company's annual Customer Loyalty in Retail Banking Report was published on Dec. 11, and it says that those who use mobile banking generally love it. In fact, while many big-bank customers score their loyalty in negative numbers, those who access their accounts and services using mobile devices on average view their banks positively. All this, and it's much, much cheaper for financial institutions to deliver services using these new technologies, compared with traditional interactions.
Not the end of the world
So yes: it's likely your credit card companies will soon begin to do all they can to tempt you into some form of online payments system. But it's hard to see a way in which they can force you to do so. If you like your credit cards just the way they are, you're probably safe.
And remember: any future changes in credit card technologies, just like the end of the Mayan calendar, won't be the end of the world.