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U.S. citizens are not required to have visas or passports to enter U.S. territories such as Puerto Rico. But Canadian citizens are required to show proof of citizenship -- usually in the form of a passport.

U.S. Citizens traveling to and returning directly from a U.S. territory are not considered to have left the U.S. territory and do not need to present a passport.

Cruise visitors must show a shipboard ID to exit and re-enter the ship.

Prior to departure from the U.S., sea travelers visiting both U.S. territories and foreign countries must have a valid U.S. passport or other original proof of U.S. citizenship, such as a certified U.S. birth certificate with a government-issued photo ID.

All Americans traveling by air outside the United States are required to present a passport or other valid travel document to enter or re-enter the United States.

While a U.S. passport is not mandatory for sea travel, it is recommended since it is a more readily recognized form of positive proof of citizenship.

The U.S. Consulate General recommends traveling with a valid U.S. passport to avoid delays or misunderstandings.  A lost or stolen passport is also easier to replace when outside of the United States than other evidence of citizenship. 

These requirements are subject to change at any time. It is the traveler's responsibility to check with the country's embassy or its consulates for up-to-date information.

Sources:
U.S. State Department: http://travel.state.gov/travel/
Canadian Consular Affairs: http://www.voyage.gc.ca/consular_home-en.asp