On the ship, they are going to be disappointed. 21 is pretty much the rule. I am not saying that they won't be able to find a rogue bartender that is sympathetic to their plight. When at a port, they will have better luck scoring some liquid libations.
I believe that is 2 liters per adult. The trick there is if you are flying. It needs to be packed in your luggage since liquids are pretty much banned from flights. Almost not worth the savings or the leakage, although I brought back a few bottles on our last cruise.
Correction on my post. There is no limit as to what you bring aboard, although they will confiscate it until your last night aboard. As for my 2 liter comment, you can bring more, however you will pay duty on that. You still have the problem of getting it home if you are flying.
Carl is correct. You can pretty much bring whatever you want back on the ship. It will be confiscated as soon as you go through the security line to enter the ship and they will give it back to you the night before debarkation. Also, if you intend to fly from wherever the termination of your cruise is, make sure the alcohol is in your checked luggage and not your carry on. Otherwise, this time it will be confiscated without a happy ending. That afternoon, a couple of security guards and luggage handlers will be enjoying happy hour at your expense.
as for finding booze more easily while at a port, i have some experience....i was 19 on my last cruise, which meant i was allowed to have beer, but no hard alcohol
however, at one of the ports (forget which - costa maya maybe?) we went on a beach party excursion that included an open bar (which, by the way, was a pretty sweet trip)...not only did the bartender not have any problem serving me tequila slammers, he also had no problem serving my 17 and 15 year old sisters