Pretty much the daddy of all submarine movies, Wolfgang Petersen's "Das Boot" takes the claustrophobia and tension of being onboard a submarine and turns it into the focal point of the movie. There's the sweaty suspense of the "silent running" scenes, in which even a moderately loud cough could lead to the sub being detected by enemy radar and death for all in the sub. In a subgenre that can be mighty unpleasant, "Das Boot" is the least pleasant of them all–and the most gripping.
The "submarine" in "The Abyss" is actually an underwater research installation, but even though there's a little more space to walk around in, the claustrophobia and tension is still rattling. Take Michael Biehn's character, who goes so nuts with cabin fever that he ends up attacking parts of the crew with an axe. Those weird glowing aliens probably didn't help matters either.
"20,000 Leagues Under the Sea"
Nemo? The guy's crazy. Spending time in a football stadium with that guy would make anybody claustrophobic, let alone on a submarine.
"Run Silent, Run Deep"
One of the classics of the submarine movie genre, "Run Silent, Run Deep" was one of the first movies to show what life was really like on a submarine. And that means tension, claustrophobia, and fear. Not just fear of being trapped underwater, but the fear of being torpedoed at any second. And it's doubtful that being trapped on a submarine with Don Rickles is anyone's idea of a fun time.