Creepy Doll by Jonathan Coulton.
The definition of the haunting song, for me, is Diamanda Galás’ rendition of Gloomy Sunday, aka the Hungarian Suicide Song.
These Dreams by Heart
Of course, in my mind, this needs to be paired with Al Yankovic’s Stuck in a Closet with Vanna White to take the saccharin edge off.
123 posts and no one has mentioned
Gentle Giant: Aspirations. The ‘for-ever…’ near the end just kills me, every time.
Collective Soul, “The World I Know”:
Winterdreams by ACCEPT
I Don’t Believe in Love by Queensryche
Hazard by Richard Marx
Fever by Judas Priest
Where Did You Sleep Last Night by Nirvana
Widowmaker by W.A.S.P.
ONE by Metallica
Yeah but as a result, I now have the earworm of “99 bottles of tears on the wall” stuck in my head. Thanks a lot. ;-D
I find Neil Young’s The Needle and the Damage Done to be quite haunting personally. I lost a lot of friends and acquaintances to IV drugs, and skated damn close to the edge of death myself in my own addict days.
The Turn of a Friendly Card, The Alan Parsons Project.
Thank you QtM, was going to post the same. I’ll stay in roughly the same lane (band-wise) with CSN&Y’s Wooden Ships.
Much of Townes Van Zandt’s discography is haunting, as is his voice and life experience. Here’s a few that stand out
Waiting Around to Die;
Our Mother the Mountain;
Lungs
Or this:
From a Twilight zone episode, or so I’ve read.
It’s about déjà vu.
Good one, @2_More_Bits . I’ve carried / occasionally sung it over the 40+ years since I first saw that ep.
I’ve always thought Home by the Sea by Genesis is pretty haunting, though the music is a bit jauntier than some of the other songs mentioned here.
The Chambers Brothers’ The Time Has Come is downright disturbing.
The version of Girl from the North Country by Lisa Moscatiello and Rosie Shipley.
Definitely Where the Wild Roses Grow by Nick Cave and Kylie Minogue
Also the Graveyard of the Outcast Dead by Frank Turner
Excellent choice. I hadn’t heard that one before. Seeing Mecano mentioned reminded me of another one of their songs that I think is haunting. Cruz de Navajas.
ETA: I tried to link to Youtube but the board won’t let me.
ETA2: That seems to have worked 
Bach, J.S. Bach - BWV 639 - Ich ruf’ zu dir, Herr Jesu Christ
Bizet, The Pearl Fishers, aria “Je crois entendre encore”. Click on “…more” for a brief synopsis and the lyrics with an English translation.
Ravel, Sheherezade - II. La flûte enchantée; III. L’indifferent.
Debussy, Nuages (Clouds), nocturne for orchestra no. 1.
Debussy, Beau Soir. English translation:
When at sunset the rivers are pink
And a warm breeze ripples the fields of wheat,
All things seem to advise content -
And rise toward the troubled heart;
Advise us to savour the gift of life,
While we are young and the evening fair,
For our life slips by, as that river does:
It to the sea - we to the tomb.