A very interesting thread, both the usual revisited arguments, and the actual lists which I find intriguing. Assuming people are being honest, it is educative to see what is, rather than what people think ought to be.
Here is my list, as far as I can remember, from the two sets the Boat Band played at the last folk club we played at: the Musical Traditions Club, at the King and Queen in Fitzrovia,London.

(not in performance order)
Trip to the Lakes (trad English jig)
Chester Castle/Chester Hornpipe(trad English hornpipe)
The Willow Tree (trad English song)
Lyme Park/Slip it in Easy (trad English jigs)
The Gypsy Princess(trad Irish tune)
Eunice Two Step(trad cajun, possibly written Amadee Ardoin)
Chere Ici, Chere La Bas(trad creole, possibly written Bois-Sec Ardoin)
Iko Iko (trad New Orleans street song)
Keswick Bonny Lasses/Stables Grand Hornpipe(trad English/Welsh?)
Je M'Endors (trad cajun)
Alfred Hughes' Waltz/Shrewsbury Waltz(trad English)
Bosco Blues(Cajun, Iry Lejeune/trad)
E Hine(contemporary Maori, can't remember name of author)
Trip to Galloway/My Love is but a lassie yet/Whitehaven Volunteers/Through the Wood Spinning(trad Anglo-Scottish)
Sultan's Polka(trad English)
Cumberland Reel/Carlisle Races(trad English jigs)
Valse des Cherokees(trad cajun).

That's about it, might have been one or two others. Wish I made lists at the time, they would be interesting twenty years on!
I hope Jim Carrol is satisfied by the high level of trad material!
All the floor singers were pretty damn trad too, but then it's a very traddy club!