'Sailor of the King' has been screened a few times on Channel 4 (in the UK), bizarrely in the original preview version with two different endings and a reminder to vote in the lobby on which one you preferred!
More votes here for Caine Mutiny, Bedford Incident and Das Boot (tv series). Couple that haven't been mentioned (some surprisingly) are Poseidon Adventure (Gene Hackman), Murphy's War and The African Queen.
The Cruel Sea
Sink The Bismarck
The Silent Enemy
The Enemy Below
Battle of the River Plate
The Yangtse Incident (also known as Battle Hell)
U-571 (historical rubbish but an exciting movie)
Run Silent, Run Deep
Master and Commander