A sweater or light jacket would be advisable for the Caribbean. For Alaska or colder destination cruises, layered clothing works best. You do not need beach towels. They will be provided by the ship. You may want to take exercise clothes along because most ships have exercise rooms or programs.
Some ships have theme nights and costume parties.
If you feel like joining in you may want to pack appropriate clothes for these events. Passenger talent contests are held on some vessels. If you want to participate, bring things like your music or a square dancing outfit etc. Cary in your purse or pocket your tickets. If doing a pier pick-up have your invoice handy although it is not necessary as your name will be on the ship's manifest.