Yes there are things to do - especially on sea days. There are trivia contests, cooking demos, dance lessons, movies, lectures, etc. There just isn't really pool parties like the original poster was asking about.
Millennium-Transatlantic-9/01, 10/03, 11/05
Zenith-Special Caribbean 11/06
Back to back Millennium 28 days - Mediterranean 11/18/07, Transatlantic - 12/2/07