Click on the name of each of the following cruise lines for their policies regarding bringing alcoholic beverages onboard:

Azamara Cruises - Wine only, maximum 2 bottles to cabin, corkage fee applies if consumed in public area. (Click here for Guest Alcohol Policy.)

Carnival - Wine or champagne only, maximum one 750 ml bottle per pax age >=21, corkage fee may apply

Celebrity - Same as Azamara, above. Also see here.

Costa - May not be brought onboard. Note that this is from the US site.

Disney Cruise Line - Yes, Disney. May be brought onboard in carry-on only, corkage applies.

Holland America Line - Wine and champagne only, corkage applies in public areas.

NCL - site is not up-to-date, but Cruise-Chat cruisers report that wine may be brought onboard, corkage applies and paid at check-in

Princess - wine and champagne only, corkage may apply in public areas. Also see Section 5, here

Royal Caribbean - Not permitted. Also look here.