Last fall we were in Maine, and my girlfriend paid for several meals with her card. The wait person took the card and brought back the receipt for her to sign. After we came back, unauthorized charges started showing up on her account.
She reported them to the bank as fraudulent. They cancelled the card and sent her a new one, but she had several automatic withdrawals on that card, so she had to change all of those to a new card.
This month she was in Panama, and she used her new card. Same thing! Unauthorized charges started to appear, so she is going to have to go through the same process of changing automatic withdrawals to yet another card.
So, when traveling, should you use cash or a card? Unless you stand right there and watch them run the card, don't use it. Use cash. Certainly don't let them go off with the card where they can copy the card, but it's best just not to use a card at all. It's too easy for someone to get your card number and start charging on it.
And you also should probably only use bank ATMs.