Good vocal duo rendition of Farewell and Adieu (to you Spanish Ladies) This one is also IMO a good rendition.
This one most defiantly I remember long ago in Music class we would have to sing this... haha!
You linked the same song and rendition I posted, haha. I'll leave the AC IV version posted to avoid redundancy. The Irish Rovers version is quite well known and popular.
I don't know the actual time period of this song, but it is a classic naval song.
You linked the same song that Blaze posted. You realize that, right?
As for other sea shanties, I don't know many sea shanties outside of the most commonly known ones or similar, but I do recall being on the Star of India ship and singin' the lyrics to Roll the Old Chariot shanty.