From Royal Caribbean's Web Site
Guests are not allowed to bring alcoholic beverages onboard for consumption or any other use. Alcoholic beverages that are purchased in ports of call or from onboard shops will be stored by the ship and delivered to guest staterooms on the last day of the sailing. Security may inspect containers (water bottles, soda bottles, mouthwash, luggage etc.) and will dispose of containers holding alcohol. Royal Caribbean's Guest Conduct Policy may be enforced, up to and including disembarkation, if a guest violates any alcohol policy. Guests under the age of 21 will not have alcohol returned to them.
Having said that we almost always bring a little something on board in our checked bags. Never had it confiscated. I have also been known to sneak a bottle of rum on board in a port. I just put it in my snorkel bag. Never had a problem with that either.