Is a passport necessary on a cruise?

It makes no difference if you get off the ship or not, you have left the country. You need some form of ID, passport is easiest but a passport card or birth certificate may work for some cruises.

Passports are not necessary for close looped cruises. That is a cruise that starts and ends in the same location. It doesn't matter if you get off or not. However many cruise lines require a passport as part of their policy. You will need one if something bad happens and you were late back to the ship. If you had to fly from one island to the next you'd need a passport. If you had to fly back to the states, you'd need one. If you are taking a cruise out of another country (for example Med cruises depart from Italy) then you'd need one to get to Italy in order to take the cruise.

But for a US citizen it isn't required.