21 for ships sailing from the U.S.
18 in Europe and elsewhere in the world depending on local drinking age.
Alcohol sales are among the highest revenue-generating factor on cruise ships. There are usually several bars on all public decks - you don't have to walk too far to get to the nearest bar

Also, beverage packages have become the norm on most ships making it possible to drink as much as you want all day long. Drink packages can cost as much as $60-100 per person per day in addition to your basic cruise fare and may also include specialty coffees, soda, shakes, and juices along with other perks that make your cruise all-inclusive. DH and I drink wine with dinner but don't consume other alcohol. I don't drink coffee at all anymore, and DH is happy with a cup or two in the morning from the buffet or room service (no charge for coffee). We don't drink soda or shakes, breakfast juices are free in the buffet or with room service, and we don't need some of the other perks that may be included with the pricy drink packages. It's safe to say that alcohol consumption is encouraged on cruise ships and the promotion of "all-inclusive" drink packages have made it easier for guests to drink all day long.