[richardwhiuk]

Social engineering once you have the last four digits of the credit card number and the billing address is almost certainly enough to score full credit card numbers. (e.g. use them to reset password for e.g. Amazon account).

[Natsu]

Not to mention that the first few will be in a certain range (or possibly with a certain prefix) depending on the card type. Oh, and the last one is the check digit.

SSNs are worse, though. The last four digits plus your birth date & location might just give the whole thing away.