Read the Consular Information Sheets (and Public Announcements or Travel Warnings, if applicable) for the countries you plan to visit.
Familiarize yourself with local laws and customs of the countries to which you are traveling. Remember, the U.S. Constitution does not follow you! While in a foreign country, you are subject to its laws.
Do not leave your luggage unattended in public areas. Do not accept packages from strangers.
To avoid being a target of crime, try not to wear conspicuous clothing and expensive jewelry and do not carry excessive amounts of money or unnecessary credit cards.
If you get into trouble, contact the nearest U.S. embassy.