You should use credit cards and ATM cards with extreme caution while in the Dominican Republic. Credit card cloning and identity theft are common when using cards in shops, restaurants and ATMs. It is much safer to use cash. Recent reports indicate that credit card fraud around Punta Cana and the rest of the country has been increasing significantly.
If you decide to use your credit or debit card, you should never let the cards leave your sight. You should also pay close attention to credit card bills following time spent in the Dominican Republic. Sometimes charges appear on your statement months after your visit in the Dominican Republic. Victims of credit card fraud should contact the bank that issued the credit card immediately.
Minimize the use of automated teller machines (ATMs). There are various techniques criminals use to get your card and your pin. ATMs inside the back are safer than the ones freely available on the street.
US Department of State has a good updated information on various crimes that have been reported by US Citizens. Similarly good up-to-date information can be found at governement websites of Canada and the UK. You should always check if the travel is advised before you decide to visit Dominican Republic.