Identity theft.

If you have a couple pieces of information (Name, address, Social Security Number) you can become anyone. I just opened an account with a new bank. By mail. In addition to the application, I needed to provide a photocopy of my SS card.

Never, ever carry it with you. In the U.S. at least, you rarely (if ever) need the original on you. And anyone who's gone through college or the military probably have their SSN memorized by now anyway. :-)