I found out today that someone has been using my AmEx card number. They've used it for airline tickets, FedEx shipping, and opening up a couple of accounts for online dating sites, I think. AmEx identified the suspicious activity and called me, which is nice. I'll have a new card in a week or so.
I think this was limited to just the AmEx card, and isn't a full-blown case of identity theft. At least I hope so!