My sister had has had a lot of trouble with this. I am getting her a subscription to Life Lock for Xmas to try and end the troubles... You should look into it, if it truly does what it claims it does, it is well worth the money. I found a promo code (RD41) that will get you a year for $99. If all they have is a credit card number it shouldnt be too bad, but if they have your social and personal info then it could be a long, bad ride. From my sisters experience, it happened once on a credit card, then a couple months later, people were opening new cards and cell phones in her name.