Many countries, including the United States, have signed an international agreement allowing visitors to use their own licenses in other nations. Before traveling to another country, contact its consulate office or embassy to find out whether your license will be sufficient; you can find the phone number in your telephone book's white pages under the name of the country. Or, you can visit the U.S. State Department website at http://travel.state.gov.
In addition, you may want to obtain an "International Driver's Permit," issued by the American Automobile Association. This document translates the information on your driver's license into ten languages. Many countries require the permit, not because it meets their requirements for a license, but because it is a ready-made copy of the important information on your American license.
Finally, if you intend to stay in another country for an extended period of time, you should check with the consular office to find out whether you'll need to apply for a license in that country. Every country will have its own rules about when a "visit" turns into something more permanent.