I don't know about age requirements, but you will need a letter from your parents stating you are allowed to travel without them. *If* you are a child, that is....
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
Most lines require that you be 21 yrs old. Some allow you to do so at 18yrs. Of the lines that require 21 yrs they have been making exceptions for married people but please check as they have in the past said no even to married couples under 21.