For US citizens on a closed loop cruise (one that begins and ends in the same US port), the minimum requirement is a birth certificate plus (for those 16 and over) a government-issued photo ID (driver's license, state ID).
That being said, a passport is what I always say is best.
If you're getting a passport a book is "better" than a card. There's nothing a passport card will get you that you can't do with just going the birth certificate and photo ID route. And it just costs you money for no gain.
If you find it necessary to cut your cruise short, and fly home from a foreign port, you'll need a full passport book.
Of course, that's if you're all US citizens.