It depends on the individual youth director. On Carnival Victory, they let me in at 18. The following year (last year) on Carnival Miracle, I was met up with some girls and guys at the nightclub (and morning trivia) who were 18 and were not allowed into O2.
All I know is about Carnival. Dunno how they do it on any other lines.
Past Cruises (all except one from NYC)
Carnival Triumph to Canada: August 1999
Carnival Victory to Canada: July 2000
Celebrity Zenith to Bermuda: July 2001 AND July 2002
Celebrity Galaxy to Caribbean (from Baltimore): July 2003
Voyager of the Seas to Caribbean: July 2004
Crown Princess to Caribbean: July 2006
Carnival Victory to Canada: August 2007
Carnival Miracle to Caribbean: May 2008
Staten Island Ferry, I mean what else in NYC is free?