The one Carnival Cruise to the Caribbean I took out of Miami about 5 years ago allowed a bottle of booze and a bottle of wine per person at embarkation. I don't recall if we had to present the bottles or not. That alone defrays the cost of what you spend on board & we drank a lot.
Cruising again on NCL in Janauary and the booze is included in the fare. May be unique to Bahamian itinerary though -