I also believe it's 16; if you're under 16, you can talk to them and they will most likely be fine with it.
They might need your parents to sign a concent form.
Royal Caribbean- Vision of the Seas- Dec. 31, 2006 - January 7, 2007
Carnival Pride- Dec. 18-25, 2005
Celebrity Summit- Summer 2004
And Many more that can't remember off the top of my head!
Cruise Lines I Have Been On
Carnival (many times)
Royal Caribbean (many times)
University of Arizona '12!