The Caine Mutiny
For me, the first time I became inerested in USNA was freshman year in high school when our English teacher gave us The Caine Mutiny to read over Christmas Break. We all groaned because it was so huge, but once I started reading it, I couldn't put it down. Nothing to do with the Naval Academy, but a great story about leadership dilemmas that officers have faced in wartime. The play and the movie are also both outstanding.
Other great books for Naval (not USNA) Enthusiasts:
Fiction
The entire "Aubrey/Maturin" series by Patrick O'Brien (Master and Commander, etc.) which is about 20 books in all. The "gold standard" for Naval fiction, IMHO. A little heavy going if you can't master the 19th century style - even though it was written in the 20th century.
Alexander Kent's "Richard Bolitho" series. Same period as Aubrey Maturin and Hornblower. More Royal Navy stories (historical fiction) from the Anglo-French Napoleonic wars.
Hornblower - everyone has heard of these. I've read them all twice.
James Nelson's books on the pirates and privateers during the colonization of America ("The Guardship", et al); Continental Navy, ("By Force of Arms", et al); and the Civil War ("Glory in the Name" and "Thieves of Mercy")
Non fiction
To Rule the Waves, written by an American, it's the story of the mother of all modern navies, the Royal Navy. Absolutely first class account of the development and rise of the RN.
John Paul Jones, written by Evan Thomas. A pretty even handed treatment of the Father of the American Navy.
And so many others...