On most cruise lines they do allow you to bring sealed bottles of water onto the cruise for your personal consumption.
The water usually is pretty safe to drink on the cruise ships but you can usually bring your own bottled water on the cruise if you prefer to do so.
Most cruise lines have changed their policies and allow you to bring sealed non alcoholic drinks onto the cruise ship.
I would call the cruise line directly to be sure on their policies but a lot of cruise ships and cruise lines now do allow you to bring bottled water and even a case or two cases of bottled water on the cruise ship.
I took a few cases of bottled water on a Carnival Cruise ship and they said it was allowed but they didn't used to allow you to do so.