Here are some of the derivations listed in the above-linked dictionary entry:

Bob Dylan's Dream - Lady Franklin's Lament
Hard Rain's A-Gonna Fall - Lord Randall
Masters of War - Nottamun Town
Fare Thee Well (Gulf of Mexico) - Leaving of Liverpool
Ballad of Hollis Brown - Poor Man
Farewell, Angelina - Farewell to Tarwathie*
I Pity the Poor Immigrant - Tramps and Hawkers

I'm hoping that there are Mudcatters who have heard both melodies of each pair, and can evaluate the extent of borrowing, as Midchuck did.

T.