Unfortunately nothing will happen (or very little) as long as the credit card companies (i.e. banks) have high paid lobbyists courting our legislative leaders so that they can get laws passed that benefit the banks more so than the consumer (the new personal bankruptcy law comes to mind).
Some states have now enacted laws that require credit card companies to alert their customers whenever a breach in security has occured that may affect their account holders. Hard to believe that they weren't or aren't required to do this to begin with.
You may also notice that a majority of the announcements regarding the lack of security of consumer data are released on late Friday afternoons.
Also, even if you stopped using your credit cards you would still have a credit report or profile that someone could acces with just a few key pieces of personal information.
Now that the majority of US consumers have free access to their credit reports annually, you can monitor your credit reports more closely. I check my credit reports quarterly (through a paid service which I'll be getting rid of now) but also use the
www.annualcreditreport.com site to check my credit reports every 4 months (I check one major CRA report every 4 months to keep a closer eye on my credit reports).
Some consumers are even going the route of "freezing" their credit reports so that no one has access to them without prior permission from the account holder.