I recently had fraudulent charges on my debit card at home. After all the bs I had to go through to dispute it and get the amounts credited back there's no way I'm using my cards in Mexico or vacation in general. We carry cash, divide it up and keep it in separate places while traveling. Then we put all but what we need for the day in the safe at the resort. Hubby always brings one card just for additional charges to our room or emergencies... And this way it's much easier for us to stick within a budget.
We've used our credit cards many times in Cancun, but only at regular business such as restaurants and the malls etc and never had any problems.
There are advantages and disadvantages of each. With a credit card, you're not carrying around wads of cash (which can be stolen, with little recourse). With credit cards, LadynTramp is correct...if you didn't make the purchase, they'll wipe the charge clean. But it's true with cash, you can't be swindled at a later date. Just takes a bit of vigilance on the part of those traveling. We use a combination of methods. We'll use the card for things at the resort, but if we rent jet skis or get something not actually ON the resort, we'll probably pay cash. And we're going to call our credit union ahead of time and give them our travel dates.