Most popular things here are varsity/intramural sports. The catch is everyone HAS to participate in at least some sort of sport. But intramurals are all what you make of them and can actually get pretty competitive. Glee Club has definitely picked up, along with many other activities that you would see on a civilian college campus.
Midshipmen like to play as hard as they work. Annapolis is not a "party school," but there are plenty of opportunities to take advantage of the nightlife of Annapolis—after you turn 21. Excursions to nearby Washington DC and Baltimore are popular. Football tailgaters are a focal point of social life during the fall semester. Midshipmen are assigned “sponsor families” in their first year that serve as a home-away-from-home during time away from the Academy; many of these relationships become extremely close. Another unique feature of social life at Annapolis is that much socialization takes place within some sort of structured activity (such as sports, clubs/organizations, student government) in addition to the bar/party/fraternity scene so central to the social life of civilian universities. The 100+ person "companies" into which the student body is divided are similar to fraternities in terms of some of their social functions.