"The Memory Remains". You're lying if you say that the old woman (Marianne Faithfull, a famous English singer and actor) singing and playing the barrel organ isn't going to keep you up at night. Something like this.
"Unforgiven II" features disturbingly nightmarish imagery. Set in a monochrome void world where a young boy grows to adulthood with his arm permanently sealed within a massive concrete wall which collapses around him as the song progresses but leaves him trapped. Highlights including the wall transforming into a giant book that sucks the young man in and snaps shut, the young man trying to get away from the wall by stretching his arm out into a long tentacle that reels him back in again, and raging fires, fountains of water and a whirling tornado emerging from the top of the shattered wall, ending with the wall transforming into a topless woman who still has the man's arm thrusting through her body. James Hetfield in particular looks absolutely demonic with his face lit from below by flickering light. Once you see it, you'll never forget it.
"Fight Fire With Fire" can also be pretty terrifying. It's a song about a nuclear holocaust. The sound of a bomb going off at the end doesn't help.
"Blackened" is pretty much the same thing.
Try listening to "One" and not imagining yourself in that situation. Watching the video is even worse. In the book it's based on, the soldier doesn't want to die, but, in a CMOA and CMOH, to go on a speaking (well, signalling) tour to show the inhumanity of war.
"The Thing That Should Not Be," with the unsettling chorus guitar and Kirk's lead giving the impression of a wailing beast, also fits in this category.
"Enter Sandman" is a song quite explicitly about nightmares. It takes the lighthearted folktale of the Sandman, and twists it into something terrifying.
"Until It Sleeps" sounds like it is about someone suffering from PTSD or some other traumatic event, or someone who has seen an Eldritch Abomination.
"Blackened". Everything about it, from the relentless nature of the music to its terrifying lyrics about a natural disaster and the destruction of planet earth. The intro scores some points for creepiness too; as if the fact that it sounds mournful and even funerary in nature, it gets even worse when you realize it's a backwards recording. The un-reversed version is just as chilling.