Firecat, one of the most haunting melodies ever, I think, is Rodgers and Hammerstein's "Bali Hai," from South Pacific.

Then there's the old Celtic ballad, "Silkie" (The Great Silkie Of Sule Skerry), which was also adapated for lament for the victims of the Hiroshima bombing.

I'd also nominate "The Water Is Wide" (O, Waly Waly).