I see we already hit The Doors (my favorites, of course), Mazzy Star, and Radiohead, but I’ll add The Sundays and Jeff Buckley. ESPECIALLY Jeff Buckley. If you don’t feel like hanging yourself after listening to that you don’t have a soul.
Veteran of the Psychic Wars - Blue Oyster Cult
Tomorrow Wendy - Concrete Blonde
Edie (Ciao Baby) - The Cult
And all of the XXX Says songs by Velvet Underground, but I think Caroline Says is the hauntingiest.
Many of mine have already been hit, but here are a few more:
Hurt - Johnny Cash cover version
Legend of a Mind - Moody Blues
Angie Baby - Helen Reddy
Dark Lady - Cher
Pick Up the Bones - Alice Cooper
Oh Life (There Must Be More) - Alan Parsons
Hello - Evanescence
Winter - Tori Amos
(a “sure…but” post)
and
“Holding on to Yesterday” - Ambrosia (sure, it has mainly a romantic theme, but there’s also the sense of loss, and evocation of an unattainable past, and the harmonizing vocals in the chorus are as close to “haunting” as I can imagine)
“No Quarter” - Zep (sure, it has its slow-tempo hard rock parts, but those keyboards, during the quieter bits, certainly lend a spectral feel to the whole shebang)
(oh oh - did I just hit on another annoying buzzword?)
“Waiting List” - Dr. Octagon (sure, it’s about someone who probably shouldn’t be practicing medicine, but again - more spooky keyboards and mixing)
“Blue Jay Way” - Beatles (sure, it’s about being lousy with directions, but it also has a very ethereal production, and the verses have a certain creep factor)
“Boris the Spider”? ok maybe not
darn you drad dog for beating me to the Caspar thing.
Bowie’s “Blackstar”? “Ashes to Ashes” would qualify if it was a little less upbeat/funky.
The chorus in King Crimson’s excellent “Fallen Angel”.
Megalomania - Black Sabbath
Queensryche, “I Will Remember”
Sent from my LG-V496 using Tapatalk
From The Pearl Fishers by George Bizet: Je crois entendre encore
Translation in description (click on “show more”).
If “haunting” can mean “hauntingly beautiful”, without anything to do with death or ghosts:
Circa 1967, when I was circa 16 years old, I heard on the radio:
A fully instrumental arrangement of House of the Rising Sun, although the radio announcer announced it by the name Casa Del Sol. It was performed entirely on strings, including bass guitar for the percussion. I don’t know who the orchestra was or the conductor.
I’ve never been able to find it on-line on YouTube. I put up a thread in this forum a while back asking if anyone knew of it, from my meager description. I got a lot of pointers to various renditions, but none was it.
More recently: Woodland Night. I didn’t know the name of this, but I put the question up on this forum and somebody found it for me very quickly.
Another haunting one that you’ve probably never heard of:
Shells by the otherwise unheard-of singer Scrappy Olivieri, guest singer on The Don Ho Show, 1965. The music suggests an ethereal interlude on the beach in a tropical paradise.
The second verse seems to suggest it’s being sung by a mermaid.
I looked for this many times on YouTube and for some reason, searching for it just now for this post, is the first time I ever found it there.
I just gave it a listen, and it is rather magical, isn’t it? 
(It’s similar to my own personal memory of a song done by … The Three Belles? - some young girls - on the old Arthur Godfrey show back in the late 50’s, “Down In Bermuda”. I heard that song as a child and have never forgotten it.)
Aggh. You got me, you bastard.
Nobody’s Fault covered by Marianne Faithfull
Where’s Johnny covered by Shawn Mullins
Taps
Chopin: Nocturne Op.27 No.1
Liszt: Sonata B Minor
Liszt: Consolation D flat major No.3
Schubert/Liszt: Ave Maria
Beethoven: Symphony No.7, 2nd movement
Mozart: Requiem in D minor
C.P.E. Bach: Cello Concerto in A Major Wq. 172, 2nd movement (largo)
Händel: Sarabande
Sibelius: Violin Concerto in D minor
John Lennon - Mother
Addendum:
Hilary Hahnis a magnificent violinist
Valentina Lisitsa is my favorite contemporary concert pianist.
Together, they are…pretty damn fine (…and not bad on the eyes either, I might add)
…and John Lennon? He was a tortured soul, but a genius who all of us benefited from and he was taken from us too soon. It was a black day the day he was murdered.I really miss him.
Deodato’s version of Ravel’s “Pavane” (For a Dead Princess) is very somber.
Who else listened to this little number?
I am wondering what some of the main musical instruments are in the accompaniment. (This may be perfectly obvious for the more musically knowledgable, but I know approximately zilch about it.) Anyone care to discuss?
ETA: I am also wondering the same about Woodland Nights, which I linked to several posts above. Sounds like mostly strings and woodwinds? Viola and cello?
In terms of a spooky sense of ‘haunting’ I do find myself a little troubled by Dead Man’s Stroll. The guy passes by a cemetery one night and sees a dead guy walking, dressed to the nines. By the end of the song the narrator, for reasons not explained, now also seems to be the walking dead.
As for songs that just had a kind of etherial quality, I haven’t seen anyone mention Hurdy Gurdy Man yet. There were of course other songs of the era that had this kind of trippy sound.
You kind of get both a kind of ghost story feel and a sort of otherworldly sound in a number of Tom Waits songs, particularly in the Black Rider album.
Thought of another song that haunted me as a child: Ervin Drake’s, It was a very good year, sung by Frank Sinatra.
It haunted me because it reminded me that no one is immortal, and one’s lifetime can speed by far too quickly, before you have a chance reflect on its significance.
My mother always cried when she heard “Turn Around.”
Now that my daughter’s grown, I know why.