If the cruise is what they refer to a closed loop...meaning it begins and ends in the United States then no, you do not need a passport. You do however need proof of citizenship, such as a certified birth certificate and an approved form of identification.
My suggestion is that even if you aren't required to have one, get one anyway and don't forget trip insurance.
Is a passport needed to sail to the Caribbean and/or Cozumel?
I strongly recommend getting a passport, even if it is not strictly required.
>> 1. You must have both (1) proof of citizenship and (2) proof of identity for all foreign travel. A passport is the only document that meets both requirements.
>> 2. The staff who examine your documents, both at check-in and upon entry into a foreign country, can scan a passport much more quickly than they can enter information from the alternate documents into their computers. Thus, you'll get through the administrative processes more quickly.
>> 3. If an emergency arises at home that forces you to cut your trip short, you will need a passport to fly back to the United States. A U. S. embassy can issue a temporary passport that's valid for one return to the United States, but the nearest embassy may be on a different island and the process may take a couple days -- not exactly the inconvenience that you want if there is a real emergency.
So do yourself a favor. Get a passport and bring it with you.
If the cruise begins and ends in the same U.S. port and only visits Mexico, Canada and "most" Caribbean islands then you don't need a passport. You will need a government issued birth certificate and government issued picture ID (Drivers license).
As others have said: It is best to get the passport and trip insurance. It will make your conscience clearer and your travel easier. However, neither are "required".
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"There is a great difference between being well traveled and just having been to many places." ~Me