Wired had a pretty good article about preventing identity theft. This sort of thing predates the Internet by many decades. It happened to me when someone stole my mail, including my bank statement, some 30 years ago and tried to cash bad checks made out to me, using a fake ID. He happened to use the same bank branch I used and was caught immediately.
There is one more tip I think is worth mentioning: Your credit card company may be able to issue you a temporary credit card number linked to your real account number. This feature is provided by several large US and foreign banks through a company called Orbiscum. Depending on the bank, you can limit the time the number can be used and the amount that can be charged. It can also be restricted to a single transaction, so that once the transaction is complete, your credit card number is useless to anyone else. Consider the one-time use technique when dealing with unknown or dodgy vendors.