Earlier only a few documents were required for passengers embarking on a cruise, since the traveller remains on the ship all the time. The original birth certificate and some form of photo id would be required – school id, credit card, social security card, driving license. In some cruise liners, proof of purchase of the ticket was also required.
From January 2008, the US government has made it mandatory for all passengers on a cruise ship to carry a passport even though the cruise may not involve any travel outside the country. In case of bad weather or any other problem, the ship may be diverted to a port outside the country and the passengers may have to fly back to USA. In such case, a passport is required to re enter the country. More details available at travel.state.gov