The only shows your teen might not get into are the adult comedy shows, and the late night shows in the various lounges, like the Quest. They do station security officers at the entrance to any lounge or the theater if there is any age requirements. The security officers will run their seapass card to verify age. All the general evening shows are open to everyone regardless of age.
Majesty of the Seas - 10/03 & 02/07 & 11/08
Enchantment of the Seas - 10/04 & 10/11
Mariner of the Seas - 10/05
Vision of the Seas - 10/06 & 09/07
Carnival Liberty - 10/07
Adventure of the Seas - 9/08
Ruby Princess - 12/09
Voyager of the Seas - 9/10
Carnival Spirit - 11/10
Oasis of the Seas - 9/13
I am a 16 year old and was 15 when I went on my cruise. I was able to get into all the shows like Quest and the Love and Marriage show. There were kids younger than me in the shows. Its not that bad except some PG-13 stuff. I can't tell you whether or not there was a restriction for the late night comedy since I never went to one of those.
Freedom of the Seas - June 2008. Hopefully the first of many cruises!