A lot of cuts off of Marvin Gaye’s What’s Going On album fit this category. My favorite example is “Inner City Blues (Make Me Wanna Holler)”.
Another song, in a completely different genre, is King Crimson’s “In the Court of the Crimson King”.
Finally, shifting genres again, there is this version of “Ocean” by The Velvet Underground.
Jeff Buckley’s Vancouver.
Exit Music For A Film by Radiohead.
The other half nominated Ghost Town by the Specials before taking it more seriously and nominating Julie by The Levellers
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Your Ghost by Kristin Hersh feat Michael Stipe
Song To The Siren by This Mortal Coil feat Elizabeth Frazier
Fortune Presents Gifts Not According To The Book by Dead Can Dance
1959 sisters of mercy
Here Comes The Flood - Peter Gabriel
Par Avion - Mike & The Mechanics
Spectral Mornings - Steve Hackett
Someone Else’s Dream - Tony Banks
We Fly So Close - Phil Collins
Hijo de la Luna by Mecano
Blue Light by Mazzy Star
China Roses by Enya
Haunted by Sean McGowan and Sinead O’Connor
Dante’s Prayer by Loreena McKennitt
I Am Stretched On Your Grave by Sinead O’Connor
You hit mine right off. I’ve heard lots of haunting songs, but this is the one that comes to mind instantly every time. I’ve talked here about the first time I heard it before. A friend and I were out on an errand when it came on the radio, and neither of us had heard it before. He immediately turned it up, I pulled into a parking lot and stopped, and we just sat there listening to it, with goosebumps on our arms. Then we put off our errand to go to a music store.
Not in a spooky sense, but still haunting and sad. Past Caring
Being a Brit, I’d never heard of the Edmund Fitzgerald, but, after hearing the song, learned the story and that made me really appreciate it.
I’ll also second Mr Dibble with This Mortal Coil’s Song To The Siren
I’ll put forward Barbara’s L’Aigle Noir. (It’s in French, but the link contains subtitles.)
I should also mention that R. Dean Taylor’s There’s A Ghost In My House is one of my all time favourites, but I’m not sure that’s what the OP was looking for…
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“Ghost Song” - Jim Morrison & The Doors
“Spooky” - Mike Sharpe
“I Am Haunted” - Indians
Adam Again: The 10th Song
Lhasa - El Desierto
The original Burl Ives recording of Ghost Riders In The Sky.
In the Air Tonight – Phil Collins
More I Cannot Wish You – Guys and Dolls
Turn Around – Malvina Reynolds
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Ocean Gypsy, by Renaissance