I don't know why I forgot The Enemy Below earlier; it's surely on just about everybody's list of favorites. Another one that I forgot: The Cruel Sea.
I agree completely with Warshipguy about Midway. The writers did a reasonable job of narrating the story, but the ship footage was utterly hokey and the airplanes were almost as bad.
I had almost exactly the opposite reaction to The Bounty. I thought Anthony Hopkins and Mel Gibson were perfect for the roles of Bligh and Christian, and the ship (if one ignored the white synthetic running rigging and a number of incorrect details) was pretty good. But the script - by no less distinguished a playwright than Robert Bolt, author of A Man For All Seasons, was dreadful. It was full of pointless deviations from the real story (which is extremely well documented) and misused nautical vocabulary.
I did like the Ted Turner-funded TV miniseries Captain James Cook, with Keith Michell. I don't recall having seen it since it was originally run on cable, close to twenty years ago; I wish it would come out on video. Same goes for the excellent PBS "Masterpiece Theatre" series, The Voyage of Charles Darwin. The ship in that one was pretty bad, but everything else about the production was so good that I didn't care. (My brother, who's a zoology professor, also liked it - a rare occasion when our interest overlapped.) That's another one I'd jump at the chance to buy if it came out on DVD.
I have to confess I'm not a fan of the Hornblower TV series (though I'm one of C.S. Forester's biggest admirers). I thought the young actor who played Hornblower was superb, the acting in general was excellent, the scenery was nice, the deviations from the plots of the books were silly, and the ships (especially the models) were - well, pretty awful. I was sent a book called Hornblower's Ships: Their History and Their Models, by Martin Saville, to review for the Nautical Research Journal. Due to budget limitations, the things were built - under Mr. Saville's supervision - by workers in the former Soviet Union who had never built a ship model before and were willing to work for about $2.00 per day. Whether that exercise constituted exploitation or charity depends, I guess, on one's viewpoint, but reading about it left me with little taste for the TV shows.
Some years ago I saw a couple of British movies on TV that I haven't seen since, but would like to. One was called Operation Disaster. The plot concerned a British submarine that, in the late 1940s, collided with an old mine and sank. The rescue team eventually brought up all of the crew except two: the captain, played by John Mills, and a sailor played by an extremely young Richard Attenborough. It was a real nail-biter. The other one, also set in the Cold War, was called Battle Hell. It was the story of H.M.S. Amethyst, a frigate that ran aground in the Yangtze in (I think) 1949, was seized by the Communist Chinese, and became the subject of a long, frustrating series of negotiations until the captain (played by Richard Todd) suddenly fired up the engines in the middle of the night and sneaked out to sea. The movie was filmed on board the Amethyst herself, "with all possible accuracy." For once that claim seems to have been justified.
And on the subject of British films - we shouldn't forget In Which We Serve. Given that it was made in 1942, it's quite astonishing in its believability. It's a fictionalized version of the story of H.M.S. Kelly, Lord Mountbatten's command in the Mediterranean. Noel Coward stars as the captain; he also directed, wrote the script, and composed the background music.
I started responding to this post thinking the list of really good ship flicks was pretty short. I'm actually pleasantly surprised at how many we're coming up with. (I notice nobody's mentioned Titanic. I guess it actually is a good movie - even a very good one. But I'm so jaded with the story that I just can't work up much enthusiasm about it any more.)