and to add to the good doctor's comments:
Before I was in tech, I was in banking and one of the sub-departments I was responsible for was the retail fraud team. Many banks have now add some sophisticated software that tracks your credit card transactions and flags for review activity that is "out of the norm" (For example, if all of a sudden, you are making big dollar purchases in Hong Kong and you never bought a plane ticket to Hong Kong, those transactions would pop up and after closer review, may generate a call to you to see if they were in fact yours).
The bank I worked at implemented a very crude version of this software 10 years ago and we caught many fraudulent charges (an increase of 40%) and were able to limit the liability of bank (and make life easier for the customer) extremely quickly.
Credit card fraud and identity theft are a multi-billion dollar businesses and you need to closely guard all of your personal information.
Key pieces, that if they get into the wrong hands can ruin your life are:
Social Security number
Date of Birth
Credit card numbers
Bank Account Numbers
With any 3 of these pieces, a bad guy can, in less than 2 days, obtain your complete credit history, contact you banks, arrange for new cards to be issued, and sent to your "new address", and then move on to bigger and better rip offs (creating bogus bank accounts, wiriting hot checks, obtaining car loans, etc) and you will spend approximately 2-3 years chasing and repairing all the damage that the crook has caused (this is the average length of time it takes).
The steps that you can proactively take to limit a bad guy's opportunity (besides holding the above info tightly) are:
Get your credit reports every year (6 months is better) and review closely
Review all statements (bank and credit card) closely each and every month
Mark you credit cards with "Ask for ID" with an indelible marker.
Never, ever ignore a collections call when you pay all your bills on time, this will probably be your 1st tip that you have a big problem.
And if you do get stung, file a police report (even though the local police may not want to take one, ask for the frauds division, that MUST accept one from you), contact all 3 credit bureaus, talk to their frauds division, they will slap a code on your report that stop any future activity and help you thru resolving the mess that your credit will become, call your bank and have them place on your checking account a "Check signature card order" on your account so that every check that comes is has to be manually reviewed and make sure that any checks they catch are stamped with the fraud stamp NOT the non-sufficient funds stamp.
I know this is wordy, but it may help it you get ripped off.