The Crown Princess supplies towels [blue & white sripey ones] If you put them in the bottom of the shower at the end of the day, they will be replaced ready for the next day with clean ones! Not sure if they're just for pool use really, but we've always taken them ashore and no-one has objected! On the beach you will see lots of fellow travellers with blue stripey towels!
Yes. Leech is right - the blue and white stripy towels are for pool use. Everyone takes them ashore too to the beach. We were in Grand Turk at Easter and their beach is literally where the ship docks and all you could see were sun loungers adorned with blue and white stripes!
Also, don't take towels for showering etc. They provide bath and hand towels for you, so more room in the cases for clothes!