Credit card cloning and identity theft are a big problem in the Dominican Republic, and the problem is only increasing, so always use cash unless you have no other choice, and avoid ATMs in public places. There are various techniques how criminals get your card and your PIN code. ATMs in banks are safer than those that are freely available on the street.
If you do use a card, keep a close eye on it and monitor it for months after, ensuring there are no suspicious charges. Victims of credit card fraud should contact their bank immediately.
The U.S. State Department has current information about various crimes that were reported by U.S. citizens. Similar information can be found on the websites of the governments of Canada and Great Britain. You should always check whether the travel is recommended before you decide to visit the Dominican Republic.