One of my favorite sea shanties: Jack was Every Inch a Sailor [0]
I play this on my ukulele while my kids dance and sing along. For an endless supply of sea shanties, look up Newfoundland folk music. Also an honorable mention: Heave Away [1]
My favourite. I suspect there are some historical inaccuracies, since most of the privateers who preyed on American shipping worked during the war of 1812, not the revolutionary war, but it's such a great song. Such enthusiasm, such bitterness! Stan Rogers at his best.
Upon the isle of Newfoundland there lived a sailor boy
He was a handsome sailor lad, his father's pride and joy
He was born on board his father's ship on a dark and stormy morn
And he helped the crew harpoon a whale on the day that he was born
I might be biased, but I really like the one the crew on Statsraad Lehmkuhl sings when the ship sails into it's home port of Bergen [0]. I believe it's based on the old shanty "South Australia" but they've changed the lyrics to be about "the coast of Norway".
[2] https://www.youtube.com/watch?v=ZIwzRkjn86w