Nirvana/Nightmare Fuel

"Polly". It's pretty creepy enough on its own, but then you learn the true story that inspired the song, and it takes on a whole new level of disturbing.
"Negative Creep" has a very chilling atmosphere to it, especially since Cobain sings that he is a "stoned, negative creep" and that "daddy's little girl ain't his girl no more", which makes you shiver over the idea of a child/teen and its lost innocence.
"Drain You" about two babies who try to drain each other...
"Paper Cuts" is a less obvious example until you discover the lyrics (NSFW). Then it becomes almost as disturbing as "Polly". . . Almost.
The music video for "Heart-Shaped Box".
It can be possible to almost fall asleep listening to Nevermind, only to be jarred back awake by "Endless, Nameless"
While "Where Did You Sleep Last Night?" in Leadbelly's original version ("The Pines") is a cheerful and jolly song, Cobain transforms it into a haunting ballad where he sings he's going to the pines where the "sun never shines" to "shiver all night long." He also adds that "a head of a disembowled corpse was found, but the body was never found." An extra spooky dimension is that this song was Cobain's last recorded song before he died.