Except for the luxury lines that include complimentary alcohol as a part of the cruise (such as the Paul Gauguin), the best policy is Disney - you can bring whatever you want as much as you want.
I brought a 12-pack of beer and a bottle of tequila. But it was funny watching people pulling their small suitcases onboard with a case of beer strapped on it!
Travel Agent/Cruise Specialist w/13 yrs exp and 48 Cruises on 11 cruise lines! Favorites: Paul Gauguin - Tahiti: Uniworld River Cruises - Europe; Celebrity Solstice-class ships; Holland America - 12-nights Baltics & Russia; RCCL - 14-nights Greek Isles, Turkey, & Croatia; Holland America - 14-day Alaskan cruisetour; 10-night Canada/New England cruise; 21 days Hawaii w/7-night NCL cruise; Oceania - 25 days in Asia; more than 3 months touring Europe by train. And many all-inclusive resorts!