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.
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.
Monster: Occurs at some point during each episode, especially whenever Johan Liebert makes an appearance.
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.
Higurashi no Naku Koro ni: All the time. A recurring noise is something that sounds like a blade slicing through the air, and you can hear a similar metallic vibration.
One common symptom of having fallen victim to the curse of Oyashiro is hearing a disembodied voice saying "I'm sorry, I'm sorry..." and footsteps.
Moments when any of the characters engage in some laughter or start screaming. Which is often.
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 song "Lilium" plays with Ominous Latin Chanting as Lucy slaughters people left and right during the first few minutes of the first episode of Elfen Lied. Also some screeching tension filled song plays whenever Nyu goes into murderous Lucy mode, or any of the Diclonius are in battle with someone and about to kill them.
Occurs in Death Note whenever Light goes into Kira mode, accentuated with his creepy little giggles.
Serial Experiments Lain had the short voiceover that started every episode: * Static* "Present day...heh heh heh...PRESENT TIME...HA HA HA HA HA-" * static*
And then there's 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.
Black Butler: Make it out of gold and silver, gold and silver, gold and silver. Make it out of gold and silver, my fair lady.
The original sound novels of Umineko no Naku Koro ni 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...
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.
Hellsing's sound of Rip Van Winkle's alarm clock ringing continuously in the fourth OVA, shortly before Alucard smashes it.
Manga have literally hundreds of unique sound effects, but the one at the end of Junji Ito's The Enigma of Amigara Fault is the one that will stick with you forever. DRR DRR DRR...
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.
In episode 11 of Ghost Stories there's the sound of a lot of phones ringing all at once and the voice of Mary, a talking Creepy Doll.
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.
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.
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.
The sound of Yuno's voice in the Mirai Nikki anime when she screams ''Akise Aru...You're...dead!" after she sees him kiss Yuki.
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 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.