In AKIRA: The sound the burst and sweeping cooling pipes make once Akira's chamber bursts out of the sound. The fact there is next to no other sound in the background, and the visuals and audio makes it clear it happens in the background and the sound really carries leaves both the characters and viewers in awe.
The roars of the Female Titan in Attack on Titan. Every single person that hears it is either shocked speechless or terrified. Sasha compares it to the screams of a cornered animal, warning the others that something horrible is about to happen. She's right.
The crunching noises made by the Titans eating, as well as the screams of their victims.
Axis Powers Hetalia: Whenever Russia is angry, he'll chant KOLKOLKOL in a decidedly creepy fashion.
Berserk: In the anime during the Eclipse the sound of Guts hacking at his arm to break free of a demons jaws with his broken sword.
In the anime adaptation of Durarara!!, the demonic blade Saika has it's very own song and it is very creepy. Not to mention Saika's voice that gets into the heads of the people who are under her possesion. A voice that can drive anyone insane. Anyone except for Anri Sonohara, the actual owner of the sword.
Black Butler: Make it out of silver and gold, silver and gold, silver and gold. Make it out of silver and gold, my fair lady.
Bleach has the sound of Shinji's Cero blast. In addition to killing the music, it's incredibly jarring and unnatural. Best of all, the scene repeats itself in the next couple of minutes so you can experience it all over again.
All Ceros sound like that. They just don't interrupt the music like Shinji's.
Barragan's Respira has a creepy crackling sound that sounds like breaking bone.
Konjiki Ashisogi Jizo, when first released, opens its eyes to the sound of a baby crying.
Grimmjow Jaegerjaquez beating the ever-loving hell out of Ichigo's face for something like 20 minutes total.
Occurs in Death Note whenever Light goes into Kira mode, accentuated with his creepy little giggles.
In Dragon Ball, Videl expects to make it to her match with Gohan relatively easily, as does the in-series audience. For the next two episodes, we are treated to her opponent of her current match, Spopovitch, brutally torturing her in one of, if not the most horrifying fights in the series.
Also, some of Chi-Chi's outbursts (has she ever heard of speaking calmly?). You'll want to turn down your volume because you'll have a massive headache even after she stops yelling.
The 2014-15 adaptation of the Stardust Crusaders arc from Jojos Bizarre Adventure adds a distorted buzzing sound along with the sound of clocks stopping whenever DIO activates The World.
The terrifying gambling drill from Kaiji; a device that attaches into one's ear, with a drill that advances a set number of millimeters whenever a bet is lost. It's said that the noise it makes is minimal, but because of the strategic location of the machine AND the psychological pressure put into the gambler, the sound of the drill steadily approaching to destroy one's eardrums is a soul-crushing torture on itself.
Mawaru-Penguindrum: Ribbit. Ribbit. Ribbit. RIBBIT. Made even worse because the one that makes it... is none other than Tabuki, of all people.
After episode 15, any kind of chiseling noises may make you want to scream and run for the hills. Poor, poor Yuri.
Monster: Occurs at some point during each episode, especially whenever Johan Liebert makes an appearance.
Kisame's sword Samehada gets in on this trope in the chapter where it gains a mouth.Samehada: "Gi Gi Gi Gi..."
Naruto's 4-tailed form (and 6-tailed) not only looks like a hell-beast, but he emits a throaty growl exactly like the Kyuubi itself, and when you consider that he is human-sized in these forms, and that the lesser forms do not alter his voice...
The lovely blood-curdling screams of the massacred Mist-nin during Obito's rampage as well as his primal screams, reminiscient of a screeching beast definitely counts.
There's an unsettling Train Crossing sound-effect that's heard during Shinji's Personal Hell Introspections (which tend to feature trains), during Asuka's Mind Rape sequence after she spots Shinji behind Kaji, as well as during the "Breakup" lines Psychological sequence in the second part of End of Evangelion.
The second you hear "TWANG-TWANG-twang-twang-twang-twang-twang-twang-TWANG", you know that someone's mind is not entirely in the right state.
When a distorted, guttural, growling noise, like the synthesis of circuits and synapses, is heard during sync sequences (and behind the incoming Harpies), one knows everything is about twenty seconds away from going all to hell.
When you hear the cicadas, something bad is going to happen.
The piercing BEEEEEEP that announces that the Eva unit has run out of internal power. Oh... shit.
The moo-like bellow when Unit 01 goes berserk and eats an Angel. We hear it again in the background during Asuka's Mind Rape.
The sound of Kuma pushing someone somewhere in One Piece especially considering what happened to the crew. Less so now, due to recent revelations.
Paprika: A buzzing sound can be heard when a Creepy Doll is first shown in what appears to be the real world, or when Paprika sees Tokita asleep.
Pokémon Origins, of all anime, has this in the form of Charmander screaming in pain as it receives a Bite attack to its neck. What makes it worse is if you read the Pokedex entries you know the Charmander's getting close to death because it's tail's flame is going out. WTF Pokemon?
Not the first time Gainax has used that particular sound effect. It was used for the Real Space Monsters in Diebuster. Which makes it no less terrifying.
Revolutionary Girl Utena: In the shadow girls' plays there's a borderline Gory Discretion Shot when one of the shadow girls breaks the other one in half. A disturbingly realistic squishy, snapping sound is included, of course.
In the movie version, the revelation of Anthy's scar during the nude sketching scene is made all the creepier when you can hear what sounds awfully like a dentist drill.
The short voiceover that started every episode: * Static* "Present day...heh heh heh...PRESENT TIME...HA HA HA HA HA-" * static*
The "Whisper" synthesized voice that's used to say the layer titles at the beginning of each episode...
The hum of the electric power transformers becomes ever more creepy as the series progresses...especially when it starts forming recognisable words.
Soul Eater has plenty of creepy moments, like Ragnarok's screaming and the moments before Asura's release. In the dark, otherwise silent chamber all you can hear is the clanking of chains. And as he awakens he scratches madly at the floor with his fingers. Eek.
Tokyo Ghoul: The erratically plinking and banging piano notes that play during the infamous scene during Kaneki's torture with the centipede somehow manages to make the situation more terrifying than it already is.
The original sound novels of Umineko: When They Cry have a Scare Chord that will weasel its way into your head and make you paranoid for hours. Not to mention the "got a new TIP!" sound effect, which probably sounds fine on its own but gets used in more than one terrifying context...
The strange, hammering-on-metal the Stakes emit in their...er, stake form. It's constantly present whether it makes sense (ricocheting off walls in rapid succession) or not (flying through empty air).
ahaha.wav. When you hear it, people are going to die. There is no escape.
That creaking door. That goddamn creaking door.
The gorram wind, either with some scary music or by itself, brr.
Made even worse in the VN when you have finished episode 4 and the picture to the menu shows Beato's golden land with only the empty wind as a sound. All that just to remind you what happened at the end of the episode...
Wolf's Rain: Cheza's screams, most likely intentional. Is that what a dog whistle sounds like to canines?
Listen very carefully to the noise in Yu-Gi-Oh! right before Marik's eye appears overtop of Yami Marik's face.