Bully in the Alley
Soon May the Wellerman Come
Leaving of Liverpool
Drunken Sailor
Randy Dandy-Oh
Leave Her, Johnny, Leave Her by Coda
Seaman's Hymn
A Collection of Sea Shanties: Roll the Old Chariot & Sally Brown
(Here's "Roll the Old Chariot" showing the whole crew singing at the Portsmouth Maritime Folk Festival. I like this visual better.)
The Reach (This isn't exactly a sea shanty, but it was sung by the same guy who lead that last song, and I think it's beautiful.)
