Eat only thoroughly cooked food, fruits, and vegetables. You will likely be enjoying foods that you have never had in your lifetime and your stomach simply isn't used to some produce, spices, and sauces. Feel free to enjoy the local haute cuisine, but if you forget your stomach remedies watch out for Montezuma's revenge. Don't forget the aspirin, allergy medicine, and motion sickness pills. You never know when any of them will come in handy.
Prescriptions are drugs and they are treated like that overseas.
Whether you're going to a tropical destination or not, sunburn is a rotten thing to get on vacation. Don't forget comfortable shoes and plenty of adhesive bandages or moleskin if you plan on excessive walking. Wash hands often with soap and water or use antiseptic hand cleanser. Don't eat or drink dairy products unless you know they have been pasteurized. Never eat undercooked ground beef and poultry, raw eggs, and unpasteurized dairy products.