We spent the first couple of hours in Athens cancelling the credit cards that Joel had in his wallet -- several locals told us that generally the bad guys take the cash and toss the rest, but to be on he safe side, we cancelled the cards anyway.
Prior to the trip we had notified the fraud department of each company of where we would be traveling so that they wouldn't put a hold on the card when activity showed up from places outside our normal circle. What we didn't do was to verfiy the phone number to use should the card get stolen. Turned out the numbers on the back of two of the cards weren't valid; one had been changed, one was an 800-number that only worked in the US. (They have collect call numbers to use outside the US). We used our laptop to access their web sites and get correct numbers, but could have saved much time had we had the numbers with us.
What has saved us real inconvenience is that I have a credit card account in my own name; Joel isn't on it. I had it and we are using it for the remainder of the trip. I also had a card for each of the accounts we cancelled which provided us the number of the account to cancel. Single travelers should keep credit cards in different bags and make sure you have copies of the card numbers somewhere other than on the card.
We will have new cards waiting for us by the time we get home.