There's absolutely no need for a doctor's office to keep your credit card on file. If someone in the front office asks if you'd like for them to file this information, politely decline. They may also ask to write your driver's license number on your check in order to help them collect if your check bounces; ask them if they can use another means of verification (one that isn't your SSN or other sensitive info).
Doctors are bound by the Hippocratic Oath to first do no harm and while they may be very good, or even the best, at what they do, the continuing parade of breach announcements in the health care area is a clear indication that many haven't a clue when it comes to information security. All the laws in the world, even the most vigorous enforcement of those laws, cannot supplant our individual responsibility for self-protection. Our identities are our assets and it is incumbent upon each of us to trust less and be covetous of our personal identifying information. Just because someone is trained to save a life doesn't mean they can't innocently put it in harm's way.
Adam Levin is chairman and cofounder of Credit.com and Identity Theft 911. His experience as former director of the New Jersey Division of Consumer Affairs gives him unique insight into consumer privacy, legislation and financial advocacy. He is a nationally recognized expert on identity theft and credit.