Hi!
There are only a few things I can add to the great tips listed above. First thing I can think of is to pack a beach bag, this will definitely come in handy when you go on the excursions and to the pool! Some extra ziplock bags will come in handy for keeping things dry in your beach bag or to keep your damp bathing suits in when you're coming home. I always pack drawstring trash bags for our dirty clothes that we accumulate throughout the cruise, then I stick the filled trash bags in the suitcases or the closet (it makes it easier to carry dirty laundry to the laundry room also). I also bring Downy sheets for the dryer when I wash clothes (along w/the Wisk tablets & lots of quarters!!!).
Bring appropriate clothing for dinner! Boys & men must wear pants to dinner!!! Luckily we had two pairs of pants for my son on our first (4 day) cruise because they will not let you wear shorts to dinner. Ladies must wear dresses or nice pantsuits (No denim jeans allowed). On our first cruise I was always cold at dinner (I'm thin-skinned), so a nice sweater that will go w/everything might come in handy.
Try to pack a lot of clothes that don't need to be ironed. There's only one iron on every two floors (if I remember correctly) and the line is long before dinner!!!! Or, get your ironing done earlier in the day if you can break away from all of the fun!!! We actually brought a little travel steamer/iron, that worked out great for us!!!
Last but not least, please bring enough money to tip all of your servers and stateroom host/hostess. Call ahead and ask what the recommendations are for your cruise. These people work their butts off and provide OUTSTANDING service (from our experience anyways!) and they deserve to be compensated well and fairly for their efforts.
Have fun!