As stated, you legally don't need a passport, since it's a closed loop cruise. You will need however, photo ID and proof of citizenship. Your passport satisfies both of those requirements. Otherwise you need your driver's license (photo ID), and birth certificate (proof of citizenship).
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)