There's one upsetting nightmare scene in which the protagonist sees his family shot in their home by what can only be described as Zombie Werewolf Nazi Goblins. The fact that The Muppet Show is playing on the television doesn't help. Quite possibly one of the most horrifying nightmares in all of film.
Then there's the one where he's seen biting a deer.
In Bad Dreams, the protagonist Cynthia, who went into a coma after barely surviving a mass suicide, is tormented by images of the dead cult leader, Harris.
In Batman v Superman: Dawn of Justice, Bruce has several nightmare sequences, the first one being the opening of the film itself, with Bruce reliving his parent's murder, and the day of their funeral, where he accidentally fell into the caves beneath the Wayne estate, disturbing the bats within. Although it's subverted with the "Knightmare", where Bruce finds himself in a wasteland that was once Gotham, as a resistance fighter against an oppressive regime led by Superman. The fact that the nightmare contains things Bruce doesn't know about at this point, such as Parademons, and the appearance of Barry Allen at the end with an Ominous Message from the Future, makes this clear this wasn't a dream, but a vision of a Bad Future.
In the 1996 film The Cable Guy, the main character Steven has a nightmare in which Chip (Jim Carrey) pounds on the door a few times but there's no answer, but later he bursts through the door and snarls, "I JUST WANT TO HANG OUT. ...NO BIG DEAL!" and chases him. This nightmare is a parody of the chase scene from Wolf.
Camel Spiders: Late in the movie, Captain Sturges is sleeping, and ends up having a nightmare about the camel spiders that attacked the (presumably) Taliban soldiers he fought in the Middle East.
In Cannibal Girls, Gloria has a nightmare where she sees Cliff being restrained and eaten by the Cannibal Girls. This serves as a bit of foreshadowing for his eventual fate.
The Day the Earth Caught Fire plays the sequence throughout the movie. What starts with two atomic bombs being activated at the same time, ends with the Earth gradually being pulled towards the Sun.
Death Wish 4: The Crackdown opens with Kersey confronting three muggers who beat and rape a girl. When Kersey kills all three, the last one he rolls over turns out to be himself. Kersey then wakes up via Catapult Nightmare.
A whimsical example in Earth Girls Are Easy: In the afterglow of her night with alien paramour Mac, Valerie slips into a Deliberately Monochrome dream that starts with a TV set screening clips from Earth vs. the Flying Saucers and, as she desperately changes the channel, the 1946 Beauty and the Beast — the latter confronting her with her romantic dilemma: Should she go with Mac to his home world, since he's leaving as soon as his ship is fixed? She then looks outside to find that the familiar faces of her neighborhood are all aliens of various sorts, and as she runs through her house in a panic there are even more creatures and robots running amok. She tries to turn to her Earthly (and unfaithful) fiance Ted for help, only to see him start attacking pre-makeover Mac as the dream dissolves.
There's a good chance that Eraserhead is entirely made out of this trope.
Two-thirds into The Fall, Alexandria accidentally falls off a shelf and bumps her head, sending her into a trippy montage merging together random fantasy sequences (including the Framing Device story she's being told throughout the rest of the film), a personal flashback to her village being raided, and a terrifyingly uncanny Stop Motion sequence of a doll being operated on (tortured?) by mysterious figures in hoods.
In The Fly (1986) Veronica (Geena Davis), having found out she's pregnant by a man who is undergoing a Slow Transformation into a Half-Human Hybrid, subsequently has a nightmare in which she gives birth to a squirming maggot-like creature. The film originally was to have an epilogue that included a Dream Sequence in which a human baby with butterfly wings emerges from a chrysalis as a hopeful counterpart to this, and answering the question of whether she would bring her pregnancy to term or not, but none of the four filmed versions of the sequence played well with the creators or test audiences so the film instead closes with her lover's death by her hand and leaves the question unanswered.
Ghost Note: Mallory has a nightmare where she enters a nightclub full of people wearing masks. When Eugene Burn starts playing music onstage, the people start attacking eachother.
Ghosts of War: The soldiers start having these once they're in the chateau, one of which is pretty much a scene of one of them being attacked, and then woken up.
In Gothika, the main character suffers two of these.
Grandmother's Farm 2: Near the start of the movie, Khalid has a Flashback nightmare about the girls he met in the previous movie, and how he took one of them, Noora, and brought her back to the farm.
Grandmother's House: On the first night living with his grandparents, David has a dream where he sees his grandpa carry a body down into the basement. He sneaks down and spies on him through a shelf covered in jars of preserves, seeing his grandpa preparing knives to cut up a woman. One of the jars falls over, alerting him to David's presence. David tries to hide under a blanket, but his grandfather finds him immediately and decides to start stabbing him in the stomach. At that point, David wakes up.
In Hollow Man, Linda is fast asleep in bed with the windows wide open. Suddenly, the bed covers slip off of her and Caine crawls onto her bed, takes her underwear off, and begins to rape her. And then she wakes up with the bed covers still on her.
In a similar manner, Rosemary's Baby, has a sequence in which Rosemary is drugged and undressed by her husband and a local cult, and then raped in her sleep by the devil. She later awakens to discover that she is pregnant, but her husband goes along with her assumption that he "went ahead and did it".
Kruel: At one point, Jo has a nightmare about Willie attacking her in her home with an axe.
The Lazarus Effect has Zoe's recurring nightmare of a fire when she was young.
Lost Creek: After meeting Maggie, Peter starts having nightmares about a distorting sounding voice calling out to him.
Mission: Impossible – Fallout opens with Ethan having one of these. It has Ethan marrying Julia in what appears to be at a lake, when the priest is revealed to be Solomon Lane, who tells Ethan that he should have killed him. A nuclear explosion suddenly appears and vaporizes all three before he wakes up.
There's another one later in the film, when Ethan's sleeping in the back of the team van on the way to London. This dream also features Julia and Lane, and Ethan wakes just as suddenly and silently, looking just as shaken.
Ethan has a vivid nightmare/hallucination sequence while traumatized and sleep-deprived in the first film as well, this one heavily blurring the boundaries between dream and reality.
The "Moloch Machine" sequence from the silent classic Metropolis. After witnessing a dreadful accident, Freder hallucinates one of the machines in the lower levels of the city is a shrine to a God of Evil, consuming the workers killed in keeping it running like human sacrifices.
Monkeybone has many - a drug that could be described as "Nightmare Fuel" is even a plot point.
The heroine in Next of Kin (1982) experiences two of these over the course of the film, both hinting at events from her childhood and the possibility of a family curse. In the first, she sees herself as a young girl wandering the deserted hallways of the Montclare retirement home while carrying a red ball. In the second, she sees a recent drowning victim swimming towards her window and tapping at it.
The entire A Nightmare on Elm Street series is themed around this, as Freddy Krueger attacks his victims through nightmares. Even worse, considering how much power he has over the dreamscape, he is able to manipulate your dreams according to your fears, desires and insecurities. Makes the glove itself feel like being put to sleep in comparison, not to mention a more merciful death at that (let's just say the multitude of freakish nightmares some of the teenagers suffer increase in frequency the further the series progresses rather than describe them).
Pee-wee's Big Adventure has two of these — in the first one he sees a stop-motion dinosaur eat his beloved, missing bicycle, and in the second there's evil clowns and even a trip to Hell! A third scene was also filmed involving a giant monkey (which is actually Francis), but was deleted.
Rambo has one of these in Rambo IV, which culminates in Trautman shooting Rambo in the stomach, which was from the original planned ending for First Blood.
The Secret Garden: Mary, at one point, has a bad dream in which her mother leaves her in a jungly version of the garden, and she's a little kid.
The dream sequence the main character in Son of the Mask has. His wife being pregnant and giving birth... only to reveal that she is pregnant with many, many, many babies, all squirming and crying with fanged mouths.
Star Trek: First Contact opens with Picard finding himself inside a Borg cube and part of the collective hive mind, before he's experimented on and his eyes are almost pierced by a needle. There's a fakeout where it seems like he's woken up, but then a Borg implant bursts out of his cheek before he wakes up for real.
Strange Nature: Kim has one about her son growing up into a deformed mutant with a half-frog face as a result of living in her town. In the dream, after eating, he goes into a small room, puts a gun to his head, and says "Thanks, mom." before shooting himself. She wakes at the sound of the gunfire.
Briefly parodied in Top Secret!: Nick's back in high school! It's the day of the big chemistry test and he hasn't studied! Then he wakes up and realizes he's actually a prisoner in an East German torture dungeon. "Thank God!"
The basis of The Evil Within is that Dennis has been having these since he was 4. He even lampshades how dreams generally lack logic, making them sound ridiculous when you try to explain them, but his special dreams, while surreal and terrifying, make perfect sense, and their narrative continues through the dreams.
The Undertaker (1988): Early in the movie, Nick has a nightmare of when he was a kid, and his uncle Roscoe makes him get closer than he's comfortable with to a dead body.
Under the Bed: Paulie falls asleep in his theater group and has a nightmare. It ends with a man with black gunk on his face popping in and shouting "Wake Up!" at Paulie, causing him to wake up and freak out.
There's a horror movie from the early '60s called The Mask (no relation to The Mask with Jim Carrey) about a cursed Aztec death mask that prompts visions like this, eventually driving the wearer to madness and murder. The nightmare sequences drip with Surreal Horror, and are easily the high point of what is otherwise a rather unremarkable movie.
The Zombie Apocalypse in Apartment 14F: Raymond and Joey have a few nightmares over the course of the film about zombies. Whether it be getting caught by zombies, or discovering Red is one of them.
A third scene was also filmed involving a giant monkey (which is actually Francis), but was deleted.