I will add my vote to "And The Band Played Waltzing Matilda" - and mention that the first recording of it that I ever heard was many years ago by an excellent group called Clam Chowder. Still affects me.

There is also "Les Vieux" by Jacques Brel, which in its English translation is known as "The Song of Old Lovers." I find the version recorded years ago by Judy Collins difficult to listen to, even to this day.

But, the song at the top of my list isn't a folk song, but Bette Midler's "The Wind Beneath My Wings." My dear wife passed four years ago; she liked Bette Midler and this song always reminds me of her. If I hear it, I will leave the room. Even thinking about it is quite difficult.