Clarifying some of the points made in the earlier posts...
If you are a U.S. or Canadian citizen, you must present your passport or a certified birth certificate along with photo I.D. when you check in for your cruise (this applies to all itineraries that Disney sails).
At all ports of call, you will need to swipe your KTTW card and show photo I.D. (such as a drivers' license) when exiting and reboarding the ship. Children under 18 do not need a photo I.D., but they must be accompanied by their parents/guardians when exiting/reboarding the ship.