I have had my credit card number used twice -- both time to buy telephone cards. Both times I reported it immediately and did not have to pay. The second time I received a new account number (what a pain!) I was told that is the comon scam -- buying these phone cards -- it was a couple of hundred dollars each time.

But far more dangerous and difficult to resolve is Identity Theft. This occurs when someone gets your SOCIAL SECURITY NUMBER and opens new accounts in your name. The use a different address and YOU NEVER KNOW ABOUT IT until you try and get credit --i.e. home loan, car loan and are denied. The other day I was in a line behind a woman and I could see her Social Security card in her wallet. The ONLY place your social security card should be is securely locked up in your safety deposit box or the like. DO NOT HAVE YOUR social security number anywhere in your wallet (my wallet has been stolen). Do not have your social security number on your driver's license.
You should treat your social security number like your most valuable possession --- it is.