Aside from Dylan's use of older tunes/themes/lyric bits, which we've probably discussed ad nauseum [sic] . . .

Some friends used to sing one called "Stay All Night" that used the tune to "Waterbound", with an added chorus. Jean Ritchie wrote "None But One" to the tune of "Nonesuch". There's also a lovely song called "Wild Geese" that goes to "Planxty John Irwin" (I think--I know the tune but I might have mistaken the title), but I don't know who wrote the words.

I've also heard songs borrowing the tunes to "Sweet Betsey from Pike", "Rosin the Bow" (many times), "Little Old Log Cabin in the Lane" (many times), and the tune used for "Sink the Bismarck", which is a march that I've seen with many sets of lyrics, going back at least to the 1860's (although I do not know where it came from or what the original title might have been).