The July 1972 issue of Popular Mechanics featured an article about the work of the research ship John N. Cobb. As the ship detoured to investigate a flock of seabirds feeding in a spot 270 miles west of Seattle, the sonar man was astonished to find the seafloor profile rising fast. Astonished, because this was an area where the sea was thought to be a good two miles deep.
Cobb had found an uncharted seamount that rose to within 110 feet of the surface. That isn't very deep for the open waters of the North Pacific. The largest oil supertanker ever built, Seawise Giant, drew 81 feet of water when fully laden.
Coincidentally, the crew of US Navy attack submarine Pogy (SSN-647) was soon to discover another uncharted mountain while on patrol elsewhere in the Pacific.
Pogy was a Sturgeon-class nuclear-powered attack submarine, equipped with nuclear-tipped SUBROC missiles. In 1984 it achieved a degree of fame when mentioned in Tom Clancy's The Hunt for Red October. In the novel, Pogy was one of two submarines escorting October back to the US.
I don't have all the details, but have heard that Pogy was running at top speed when the incident happened (Fall 1972), or about 30 knots. It struck the mountain once, perhaps followed by a second, glancing blow. It was violent enough to throw sailors to the deck and to cause considerable damage to the bow section.
In some respects Pogy's crash was more severe than the fictional one depicted in The Abyss; but in this case, submarine and crew survived. The crew was able to reach the surface by using the emergency-blow system installed in submarines built after the April 1963 loss of Thresher. Pogy went to dry dock for repairs, perhaps at Point Loma, CA.
The PM article describing Cobb's discovery can be found on Google Books, here. As far as I know, Pogy's close-call incident has not appeared in the public literature, other than as a few brief references by crewmen (years later) to an impact with undersea terrain.