Just got curious and checked my iTunes tracks in order by playing time. Looks like the longest single song track I have is Jody Stecher singing Barbary Ellen, at 12:45. It's on his album, Oh the Wind and Rain.

In terms of tune sets, there's one at 27:38 from Martin Hayes and Dennis Cahill, on the Live in Seattle album.

The longest combo song and tune set I have is The Green Fields of America on the album Kilkelly (Moloney, O'Connell and Keane) which clocks in at 21:24. (I'm afraid the song Kilkelly itself on this album comes in at a measly 6:47.)

And for honorable mention, Jean Ritchie's version of Little Musgrave is 12:03. (That's on her album Ballads from Her Appalachian Family Tradition.)