I have a few friends who have had this happen - on Amex, bankcards or other plastic - generally it happens due to the fact that very few of your personal details are actually checked by most organisations, although there should always be decent checks.

It's so easy for folk to get your credit card number these days. Even at some local shops, the till displays it along with expiry date and anyone can memorise a 16 digit number.

The upside, at least in the UK, and probably elsewhere, is that the onus is generally on the bank to prove you did make the transaction, so none of my friends has been hurt by this (other than indirectly through higher charges, I guess)