The Police/Nightmare Fuel

Hints in many songs, but "Synchronicity II" is probably the most nightmarish of their singles.

Many miles away
There's a shadow on the door
Of a cottage on the shore
Of a dark
Scottish lake...

"Friends", a song about a man who befriends people and then eats them.
- In a similar manner there's "Murder By Numbers" which is a jazzy tune about a serial killer.
- There's also "Once Upon A Daydream," with copious amounts of Lyrical Dissonance. Perhaps not coincidentally, the previous three were all written or co-written by Andy Summers.
"Masoko Tanga", which is the Last-Note Nightmare for their first album. Sting has (perhaps jokingly) referred to being hypnotised while playing the song, saying that the gibberish lyrics were cries from a past life.
"Shadows in the Rain" a song about schizophrenia (or heroin addiction) which is pretty much made of Fridge Horror.
"Tea in the Sahara," which ends with three sisters dying of thirst in the desert.