Norwegian Cruise Lines is the main cruiseline operating out of Honolulu and Maui, and they stop at all of the islands. I don't believe any start on the big island, although I know they do stop there. Look online for Regal Travel and Nonstop travel - those two travel agencies sell tickets for the cruiselines. There are two lines - the Norwegian Wind - a 10 day cruise to all the islands and one island south of Hawaii - so you will need your passport. The other ship is the Pride of America (or pride of aloha - sometimes it changes) - that is a 7 day cruise, and only operates between the islands, so you don't need your passport. The Pride of Hawaii should be starting soon as well. Check
http://www.ncl.com for details.