As far as I know the only one is the Disney cruise line. My son and his friends did it during spring break 2004 and had a great time. They did the 4 night cruise out of Port Canaveral. Since the Disney crusie line is more expensive they got an inside cabin and said it was fine. You're not in the cabin that much anyway. Check it out .
On Princess, anyone under 18 must travel with someone 21 and over. If you are already 18, you shouldn't have a problem on Princess.
Carnival Elation March 11
Carnival Imagination Sept 07
Carniival Sensation Dec 06
RCI Sovereign of the Seas Sept 06
Carnival Miracle Sept 05
Carnival Glory Sept 04
Carnival Fantasy Jan 04