And if you order a juice at a bar it will cost you.
Bottled water is available at bars for a fee. Ship's water is perfectly safe to drink and it is what I use.
Also, in your cabin you will find several cans of sodas and a bottle or two of water. If you use them they will be charged to your account at standard bar prices.
It isn't hard to find something to drink that doesn't require you to fork over your cruise card. Although Royal Caribbean is quite strict about bringing personal beverages aboard, some people will bring along those little packages of powder (like Crystal lite) and their own insulated mug. You can always get ice and water so they make their own flavored drinks. There is one thing free at a bar...a glass of ice water! Sometimes they'll put pitchers of it and glasses on a table near a bar or by the pools for self-service.
If your cabin has a refrigerator, grab a couple cartons of milk in the buffet at breakfast and stow them in the cabin.