All depends what cruise you are on,usely during school holidays [summer] they call it a family cruise and put on extra staff for the kids.
Just back from a week on the Black Watch. FO had laid on childrens hosts, and each night we received a list of the childrens activities for the next day, these included a welcome session, quoits & shuffleboard, a tour of the 'public' areas of the ship, pool sessions (parent to be poolside), craft & pizza making. This isn't a comprehensive list, we rarely wanted to use them (but were happy when we did) I think there were also films, board games and introductry bridge!!
There were adult / child only times for the pool, mostly general use though. There was also a childrens dinner menu if you didn't like the main menu (ask for both at breakfast).