OK, you aren't going to believe me, but we took the Disney Cruise for our honeymoon and hardly saw kids. Don't get me wrong, there were plenty of them on board, but here's what Disney does for their adults:
1) Adult only pool (most cruise ships have this)
2) Adult only restaurant (specialty restaurant - when we went it was $5 per person to eat there)
3) Adult only beach on their private island - Great, since there won't be a lot of "kicking up" of the water for pleasant snorkeling. In the family beach, by the afternoon, you can't see anything in the water, since there are so many kids murking up the water.
4) I think the improv comedy at night was adult only too
There are so many things for kids of all ages to do (there's a teen only beach on the private island too), that they are never in your hair.
I don't have any experience with Celebrity, but I have heard that they usually have less kids also. I even saw a brochure for them once that offered adult only cruises (not very often).
Star Princess - December 2006
Adventure of the Seas - April 2005
Caribbean Princess - July 2004
Golden Princess - March 2003
Disney Magic - October 1998