Little Musgrave -- became Mattie Groves when he crossed the Atlantic, but still gets murdered for sleeping with a rich man's wife.
Lord Randall -- eventually became Bob Dylan's Hard rain , but with the same "call and response" verse structure.
The Outlandish Knight -- a story found in song across Europe, and related to Bluebeard. Young woman marries bloke, discovers bodies of previous wives, either locked in a room or hanging from a tree.
The true-hearted girl/boy/young sailor/young soldier/young cowboy cut down in his or her prime -- a song about venereal disease. Became St James' Infirmary. Most versions share a verse about funeral arrangements -- something along the lines of "six bonny [somethings] to carry my coffin, six bonny [somethings] to lower me down...."