Baccano!'s Ronnie Schiatto reveals his true form in the light novels once. No physical description is given, however, on the basis that the sight was so terrifying and incomprehensible that it was blocked immediately and entirely from the spectator's memory.
Implied regarding goddesses and demons Ah! My Goddess; because they exist in a twelve-dimensional state naturally, four-dimensional beings such as humans cannot truly perceive them. This was most openly stated in chapter 268 where a demon purposefully forced Keiichi to witness a bit of her true form and nearly shattered his mind.
Mokkurkalfi: You don't perceive our true appearance. Your existence and ours are different. My form, and what you think you are seeing, are not necessarily the same.
Several characters in A Certain Magical Index have "unexplainable" abilities. Ollerus (a ridiculously powerful sorcerer) and Gunha Sogiita (Level 5 esper) are a couple... Gunha doesn't even know how his own abilities work (he thought he figured it out at one point, but was told that he was wrong). This is actually a great boon to these characters, as if your opponent doesn't understand what they're being attacked with, they cannot form an effective defense against it.
The enigmatic being Aiwass. When Accelerator gets his ass kicked by it, Accelerator has a difficult time comprehending what his foe was.
A Majin wields power that very few can understand. When Othinus (a true Majin) and Ollerus (a "failed" Majin) have a brief battle, bystanders can tell that something happened between them, but they cannot explain what.
It's often said that Galactus doesn't actually look like a gigantic human - it's just your brain that makes it that.
Turns out he was a Human Alien in the previous universe before he became Galactus, but now his true form resembles a star.
To Beta Ray Bill's people, he looks like a giant amoeba. Interestingly enough, Bill himself sees him like Earthlings do.
In one instance◊ when Galactus appears before a large number of species, the page is filled with numerous smaller pictures showing how each species perceives him. Some of them do look pretty horrifying.
Left behind in the space where the "merger" took place is an egg that will explicitly become the center of a new universe someday. Make of this what you will. (At any rate, it certainly gives Big Bang a whole new meaning.)
Toyed with in the tale of Orpheus in the Sandman Special, reprinted in Fables And Reflections. Orpheus visits Death and becomes confused and disoriented when he sees her in her house clothes (i.e. her usual 80's-90's look). She quickly cleans up for her visitor (though it's more of a 18th-19th century dress than the black Greek toga she was seen in earlier in the story).
Due to miscommunication at DC, the death of the New Gods in The Death Of The New Gods were completely contradicted by the death of the New Gods in Countdown to Final Crisis. Grant Morrisonsays they both happened, and are merely different mortal viewpoints of an event completely beyond our grasp.
Doctor Strange. The Vishanti, a trio of higher entities who sponsor the office of Sorcerer Supreme, explicitly state that they cannot show their true forms to mortals because it would wreck their minds.
In Guardians of the Galaxy, it's explained that forces and entities, like the Abstracts, sometimes simplify themselves for mortals in order to get their assistance. In the some issue, it's revealed that the setting, what looks like a giant checkerboard-like world, was actually the cloak of a gigantic Abstract.
In the Pony POV Series, the Elders of the Alicorns and Draconnequi are Eldritch Abominations (though the Alicorns are benevolent), and as such cannot be properly viewed by mortals. This is best exemplified when Liarjack meets the Father of Alicorns — the only thing she's able to view him as is a piece of the Night Sky in the shape of a pony (probably due to him being the Anthropomorphic Personification of existence). Everything else about him is so seemingly contradictory (such as appearing as a foal, a colt, and a stallion all at once), she's incapable of understanding it, and finally just gives up trying to in frustration.
The Bound Destinies Trilogy: Both times Din, Nayru, and Farore make actual appearances, they use human forms, explaining that their true forms are beyond mortal comprehension.
In Dogma, God manifests twice in A Form You Are Comfortable With (most famously as Alanis Morissette), but His/Her voice is a perfect example. Humans' heads and chests explode upon hearing it because we do not have the aural capacity to handle its awesome power, which is why God usually sends an Angel to communicate with humans.
The Metatron: We went through five Adams before we figured that one out.
The angels in His Dark Materials are described as being like this - humans and even witches see them as human shaped, being incapable of perceiving their true form which is more like architecture. At least until Baruch and Balthamos come along and really do seem like nothing more than slightly snobby see-through humans.
Death gets this whenever he interacts with humans, who seem confused because someone is talking to them, and it appears to be a skeleton in a cloak, but that's ridiculous, so the mind just rejects it. Children, however, aren't nearly as mentally fixed, so their minds easily wrap around it and they see him as he really is.
And there are occasions when Death CAN be seen. Most notably, in Wyrd Sisters, when Death decides to take the place of an actor who is supposed to play him in a Macbeth expy, everyone in the audience is expecting to see death and, therefore, does. Death, not being used to such a large audience, gets stage fright. And it is hilarious.
Non-magic users, not having octagons in their eyes in addition to rods and cones, cannot see octarine, the eighth colour; instead, they only see blackness.
Mostly averted in H.P. Lovecraft's works as his Eldritch Abominations tend to appear in their true form, which tends to lead to madness in those who see them. Sometimes it's played straight, though:
Yog-Sothoth is perceived by mortals as congeries of iridescent spheres because his true body transcends the space-time continuum and we only see the small parts of it that happen to intersect with that particular location in time and space.
Nyarlathotep tends to appear in a form of a man because it makes manipulating humans easier. He has several less human forms too (1000 to be exact) but all of these are just avatars, or "masks". What his true form looks like is never even hinted, but as he is the soul of the Outer Gods, he might not even have a physical body outside the avatars.
Although it's never explicitly mentioned, considering the insignificance of mankind in Lovecraft's cosmology it's very unlikely that the Elder Gods naturally look humanoid. More likely the human-like forms they appear in are used by them in order to not drive humans insane. The Elder Gods oppose the Great Old Ones, and since mankind would be destroyed if the Old Ones awaken, they are the closest thing the Derleth-subscribed mythos has for benevolent deities. Not that that's saying much.
In "Through the Gates of the Sliver Key", Yog-Sothoth explicates a major implicit premise behind the whole Cthulhu Mythos: practically everything we experience goes under this trope, including three-dimensional space, change and time, and the individuality of what we ordinarily think of as different creatures. Ramsey Campbell's "The Render Of Veils" exploits this variation of the trope to very disturbing effect.
In the Otherland series by Tad Williams, Felix Jongleur communicates with The Other through simulations so he can avoid interacting with it more directly. Unusual in that he's the one who determines what fake form he's perceiving, though The Other tends to warp the simulation into something a bit more disturbing.
The NA Sky Pirates! features a small pocket universe that is one of these, which is hiding a totally separate species that is also one, and it also heavily implies the Doctor himself falls into this category. Its loose sequel Death and Diplomacy extends this to the TARDIS too.
The Ellimist always appears in a humanoid form before the Animorphs, while his true form is some techno-organic behemoth made out of countless pods, organs, feathers and the like, built around his original avian body, about half of which is still trapped inside a black hole.
Angels are like this in C. S. Lewis's Space Trilogy. Most of the time they just look like a vague shimmer of light; other attempts have produced wheels rolling on distant hills, a painful impact of colors (described as being like the "true sensation" of being hit in the eye by a rock), and (most successfully) a pair of otherworldly humanoids.
In Ambrose Bierce's "The Damned Thing", there is a creature that is not of alien form but of alien color rendering it impossible to see properly.
In Larry Niven's Known Space series, Hyperspace has this quality: the human brain is completely incapable of perceiving hyperspace, and carefully edits it out of your sight, and in about 60% of humans drives them insane. If you look at a window, you see the frame basically collapsed all around the window, which is slightly less disturbing. And if you look at a 360 degree panorama or hyperspace, you lose sight completely: you don't just go temporarily blind, your completely forget that you ever possessed sight, or what sight even is.
A particularly nasty variation happens in Harry Potter, in the Boggart that takes the form of whatever you happen to fear most.
In The Dresden Files, there is a semi-divine being known as a Skinwalker, or Naagloshii. Just to look at it resembles a powerful bestial creature (with the ability to shape-shift). Certainly frightening, but by no means incomprehensible. However, when Harry uses his Wizard's Sight on it, even briefly, the effect is almost mind-shattering. The Naagloshii's true form is so inherently wrong that it literally takes hours for Harry to dissemble enough to function normally again (and he has to be careful not to think about it otherwise it reduces him to near unconsciousness).
It is implied that the powerful movers and shakers of the supernatural world have similar (if not so utterly abominable forms). The Queens of the Sidhe, particularly Mothers Summer and Winter, are beings of such intrinsic power that their true forms are likely to be completely incomprehensible.
He Who Walks Behind is so alien that even his name cannot be comprehended, merely experienced as a rush of ugly emotions and a deep-seated hatred for all mortal life.
Played straight and subverted in Dan Abnett's Know No Fear. While fleeing from Chaos Daemons two Guardsmen perceive them as horrific monsters with horns, spikes and forked tongues. However one member of their party, the seemingly immortal Oll Persson thinks to himself that what they are seeing is not the true form of a Daemon, it is what their minds are perceiving it as by pulling together bits of what they believe monsters look like. He however sees their true forms as shapeless clouds of warp energy and is able to kill them.
The various dieties in The Elenium and its sequel series The Tamuli are hinted to be this, seeing as Aphrael can appear as a child, a grown woman, and even two people at the same time.
In E. E. "Doc" Smith's Lensman series, it is impossible for anyone to properly see a Palainian or any other being that lives in distant planets that are perpetually cold. This is because these beings survive by being four-dimensional (this is described as a "hyper" dimension); since everyone else lives and perceives in three dimensions, this extra-dimensional aspect is lost on them.
A variant of this happens in Life, the Universe and Everything, when the giant supercomputer Hactar appears on a psychiatrist's couch. The couch appears the normal size for a couch, the computer appears the normal size for a giant spacebourne supercomputer, the illusion that one is sitting on top of the other is ... disturbing.
The Last Dragon Chronicles: Happened to Gwillana when she seen the inverted version of Gawain's head. She died from the sight of the thing.
In Babylon 5, most people see the Vorlons as whatever equivalent their culture has to "angel," but Londo apparently sees nothing. Whether this was because the Vorlon ignored the Centauri race and focused their ancient genetic manipulation on the now-extinct Xon race that also evolved on Centauri Prime, or because Londo is just a Jerkass, is never explained.
JMS claimed somewhere, in response to a fan's question, that Garibaldi (an agnostic) would have seen himself in Kosh. This statement seems to support the idea that it was Londo's having been touched by Shadows that led him to see nothing, rather than any faith-related matters/crises on his part.
Parodied somewhat in The Middleman, when MM and Wendy visit the underworld. It appears to Wendy (and the camera) like an office building, but when she mentions this to MM, he claims to see an overgrown field full of feral creatures. He's kidding, he sees an office. "Someone's funny in the underworld."
Many portrayals of the Q Continuum, including the episode "Death Wish" of Star Trek: Voyager, indicate that whenever a human enters the Continuum it looks like normal 4D space-time so that the human mind can comprehend it. In that episode, the crew joins the Q Continuum rebels against the Q old guard. Because the humans (and aliens) cannot comprehend Q weapons, they perceive the situation as the American Civil War... even the weapons they're using against the old guard Q. (Tuvok threatens these Q with their own weapons after being insulted.)
The novel I, Q goes so far as to say that the human mind does this automatically to stay sane and that Data normally shuts down because his android mind tries to "see" everything and crashes. Q must filter the sensor input so Data can function.
In fact, the Q Continuum has never been truly perceived by visitors; they're always shown a representation which they could understand.
In one novel, Picard perceives the Continuum as a weird-looking highway with a sign at the on-ramp saying something like "Organians, keep out!"
The book also mentions that the Q don't like the Organians for their smugness and the holier-than-thou attitude. Which is like a teapot calling a kettle black. Is there anyone in the galaxy more smug and self-righteous than Q?
In Supernatural, angels cannot be comprehended except by their true vessel. Anyone else who glimpses their true form has their eyes melted out of their head, and anyone else (or anything around anyone else) that is around their true voice experiences what basically amounts to tornado conditions. To even be comprehended, they must first take a vessel. Any improper vessel, even the next closest thing, will eventually explode under the power.
Archangels are even worse. The very presence of their true form is capable of doing all of the above, but with massive earthquakes, and instant death for anyone who's around.
And this can even remain true when they're in a vessel. Raphael simply manifesting himself created a thunderstorm that knocked out all power to the Eastern Seaboard. In a later episode, he similarly created another thunderstorm when he manifested again. And when he showed up to protect a prophet, the growing light was tearing the room apart.
According to Zachariah, his true form has 6 wings and 4 faces, one of which is a lion. This is actually in line with how The Bible describes angels.
In Grimm, it's explained that it's generally a bad idea for normal humans to see the true forms of Wesen, as it could make them Go Mad from the Revelation. Someone like Hank whose sanity was able to withstand the initial shock then thinks he was going crazy. For weeks, he was unable to sleep and was becoming increasingly paranoid. Nick had to stop him from shooting his own goddaughter in a blind panic when she accidentally reveals her Game Face.
The Weeping Angels from Doctor Who, maybe. They can't be seen by any living being, and any time they can be observed, they instantly freeze into their trademark stone statue forms. It's implied, however, that they aren't necessarily limited to the form of angels when frozen in stone. We don't know why they freeze into rock beyond it being a defense mechanism, but for this very reason, what they are/look like unfrozen is anyone's guess.
Observer in Mystery Science Theater 3000 insists that he exists only as a brain, and that if "lesser minds" perceive a body carrying around said brain, it is merely this trope in action. (All evidence in the show suggests that yes, he does have a body, although his brain is indeed outside of it.)
Religion & Mythology
The Bible, in the Old Testament, God warns Moses that "you cannot see my face; for man shall not see me and live". Even Moses, could only see His back. God, like Yog-Sothoth, also is omnipresent and exists at every point in the space-time continuum simultaneously yet transcending all of it, and Jesus is just A Form You Are Comfortable With. Islam takes this bit particularly seriously; arguing that if God's true form is alien and utterly incomprehensible to humans, then you cannot picture Him as anthropomorphic, therefore doing so and worshipping God through pictures is considered blasphemous, heretical idolatry (Christianity under the Byzantine Empire also tried this but failed).
Which then rubbed off on Moses a bit, since when he came back to everybody else his face blinded them into making him wear a veil.
That said, several Old Testament figures (including Abraham, and for that matter Moses) are said to interact with God directly. The usual explanation is that they were speaking with an angel who was speaking directly for God (acting as a kind of cosmic telephone), or else that God was appearing in a form they could comprehend. Christians often interpret these events as pre-incarnate appearances of Christ, the "image of the invisible God".
In another incident (Exodus chapter 24 for those who care) God appeared in full glory for seventy-four leaders of Israel total. The fun part? It mentions that they all ate and drank together. And it says that God stood on a sapphire pavement. And absolutely nothing else.
Notably, this is subverted in the Catholic faith, as the saints will get to see God in all his glory in Heaven, often referred to as Beatific Vision. The idea behind it is that it should destroy your very soul, but God, being God, could perserve someone from letting that happen. (Or perhaps that "no man sees my face and lives" isn't so much of a concern if you've already died...)
Also applies to the Seraphs, God's personal throne guards. They keep themselves hidden with their wings (they have six or more, by the way), as any mortal who looks at them directly bursts into flames or get annihilated instantly.
Regarding Heaven, some believers reject a Fluffy Cloud Heaven and Fire and Brimstone Hell interpretation of the afterlife, instead preferring a metaphor-based no-true-form spin on where we cannot really comprehend the true form of those dimensions, and the literal interpretations above are just approximate interpretations of what is really happening in there. For example, Heaven is a state that is expressed in metaphor as a place of peace and bliss, while Hell is filled with so much of all kinds of sin, chaos, insanity and perversions against nature that the human (and supernatural) mind is unable to cope with it, and tries to resolve it into a Hell it can comprehend and express in art, namely a dark inferno filled with pain and disgusting Eldritch Abominations.
Averted with Jesus generally, although revealing Himself to Paul later on (after the Ascension), is likened to a lightning strike and knocks Paul off his horse, temporarily blinding him.
Some forms of Gnosticism play this straighter, teaching that Jesus never was physically incarnated, and had no tangible form.
The New Testament condenses all of its incomprehensibility in the book of Revelation. Okay, so the four horsemen and great seven-headed beast are all probably metaphorical... and maybe angels in their native environment really are humanoids, some with six wings and using four of them to cover their faces and feet, or have four wings and four faces... but then John talks about things like how "the sky rolled up like a scroll," and you start to get an inkling of how everything this poor man's mind was experiencing utterly defied all human comprehension.
Older Than Feudalism: In the Bhagavad Gita, Krishna actually shows Arjuna his (God's) true form, which is basically a more extreme combination of Eldritch Abomination and Purity Personified. Krishna even mentions that Arjuna's mortal mind cannot comprehend all that he is, so Krishna briefly gives Arjuna divine sight so that Arjuna can comprehend. Arjuna still can't handle it, and begs Krishna to retake human form.
Played straight in Judaic and Talmudic literature, which says that God is incomprehensible. Oddly enough, some Kabbalistic poems describe him as though he were a human king, though the rabbis dismiss this as an elaborate metaphor.
This is exactly what happened to Dionysus' mother Semele, one of Zeus' lovers; Hera tricked her into doubting that he was truly who he claimed to be, and she insisted that he reveal his true form. Due to an oath he made to fulfill a promise to her, he had to comply. He managed to save her unborn child however, placing him under the skin of his thigh until he could be born.
In The Qur'an Moses asks to see God, who replies that the sight of Him to a living mortal would be too much... but He will reveal Himself to that mountain over there — which immediately crumbles to dust.
In the theological theory of Pandeism, it is proposed that those who are somehow able to contact the mind of our Creator as it unconsciously underlies our Universe find that experience so incomprehensible that their tiny human minds automatically defend themselves by interpreting such encounters as conscious communications from culturally familiar conceptions of gods, thereby explaining all revelation and scripture.
Dungeons & Dragons has the Obyriths, the primordial race of demons spawned by the Abyss eons before life arose on the Material Plane. Their bizarre, horrifyingly-alien appearances grant the Obyriths an ability called "Form of Madness," which causes anyone who so much as glances at them to be afflicted by an oftentimes permanent type of insanity (phobias, feelings of being consumed by insects, etc).
It's actually even worse than that. It is explicitly stated that you don't even have to actually see them to be affected as "their presence is an affront to all five senses". Even merely hearing or smelling an obyrith is enough to drive one over the edge.
Pale Night, the so-called Mother of Demons, is ancient even among the surviving Obyriths, but lacks the "Form of Madness" rule. She appears as a feminine figure wrapped in a white shroud blowing on a spectral breeze, which occasionally shifts to almost reveal what's underneath. This is neither her true form, nor a conventional illusion - instead the veil (which she can suppress with some effort) is a sort of cosmic censor, because her actual appearance is so horrifying that reality itself refuses to accept it. Pale Night's "Truth Behind the Veil" rule means that anyone who gets a good look at her true form must make an immediate (very high) saving throw; success means that the character's mind refuses to comprehend what they're looking at. Those who fail die outright, and if revived remember nothing of what they saw beyond a feeling of sheer horror.
Even some incredibly powerful forces of Good cannot be viewed safely by mortals. The Book of Exalted Deeds sourcebook mentions Zaphikiel, the greatest of the Hebdomad and the ruler of Mount Celestia. Only the gods themselves and the other Hebdomad can look upon him safely; anyone else who does so is said to be consumed by his overwhelming radiant energy and destroyed uttely. (Or maybe ascended to a higher form; it depends on who you ask.)
Predators, a book for Werewolf: The Forsaken, introduces a being known only as the Unseen, which is Exactly What It Says on the Tin. It's said that its form is so blasphemous that reality itself refuses to show it (just like Pale Night). The Unseen is uncannily good at hunting werewolf packs, to the point that some suggest it's a weapon created by a werewolf-hating Eldritch Abomination. About the only way you learn of its presence is when your guts spill out of a seemingly spontaneous slice in your flesh.
Also Hell, as presented in World of Darkness: Inferno: a place comprised of so much depravity, so much sin, that the human (and supernatural) mind is unable to cope with it, and tries to resolve it into a Hell it can comprehend. Hell's corruption is so pervasive, even looking at it triggers a check on the Karma Meter, as it worms its way into your soul.
Mage: The Awakening presents magic in general and the Supernal particularly as this. The actual underlying processes of magic are beyond human beings' ability to understand, so there need to use metaphor and symbolism to compose their spells. For those few mages who become capable of entering the Supernal itself, it's necessary to expend great effort to force it into a comprehensable symbolic form, or else unfiltered contact with it will utterly obliterate the mage. One of the goals of Ascension is to achieve a state in which true perception of the Supernal is possible.
Words describing it fail. Pages relating it shrivel. Tales recounting it end.
The Trope Namer is EarthBound. "You cannot grasp the true form of Giygas' attack!" It's a tradition of the series's final bosses. In MOTHER, Giygas (aka Giegue) attacked telepathically and without lifting a finger; his mental power was so far beyond the protagonists they couldn't process what he was using for PSI. In Earthbound he was "reduced" to anEldritch Abomination so large and all-encompassing, you simply couldn't tell where his attacks are coming from; in gameplay terms you were fighting against the background.
The Masked Man may also have this attack in the form of a laser attack that the game doesn't even say anything about.
In Pokemon Mystery Dungeon: Gates to Infinity the Bittercolds attacks are implied to be this. Ontop of the Bittercold being an Outside-Context Villain, it also uses attacks never seen in the Pokemon franchise before, hits the entire room, can confuse or vastly lower your party's stats, and the names of said attacks don't appear in the message log at all.
The power of Houjuu Nue from Touhou is this minus the Go Mad from the Revelation part. She can also imbue other things with the same characteristic by placing a "Seed of Non-Identification" on them, although knowing what the actual object is prevents it from working.
An example of Truth in Television, but here because it's caused by one: as said in the Bullet Hell page, in Touhou's Imperishable Night, some parts are so complex that your brain will actually stop interpreting data on some parts of the screen, and you can feel it happening.
When the time gets really low, some patterns are made to get very hectic; some spellcards aren't designed to be timed-out, which is what happens when they aren't beaten before the timer zeros. These final forms in the last few seconds are so intricate that they defy comprehension at times.
Team Fortress 2's Mildly Disturbing Halloween Mask "appears as a moldering, eldritch veil of such manifold depravity, the human eye will not process the sheer enormity of its malevolence, and out of self-preservation will merely show you a brown paper bag with a team colored face painted on it."
In The World Ends with You, it's impossible to make out the Composer's exact features, even though you can clearly tell who it is. He appears in a shroud of white light, and the artwork is sketchy and hard to focus on.
Parodied in Another Day, where it's explained that the appearance of a certain character is entirely because the player refuses to see the truth.
The Wave Existence from Xenogears is a fourth-dimensional being that humans are unable to comprehend, and he appears as a vaguely star-like... thing from which waves emanate similarly to the ripples on a pond's surface.
And even then, the master, creator, and lord of the Schwarzwelt, as well as the mother of all life on the planet, radiates such immense power that it's utterly impossible to recognize its form. Only by receiving the "brilliance" of a traveler of the Schwarzwelt can you get a glimpse at its true form.
The bonus boss Yggdrasil has the ability to do something "almost imperceptible" (i.e. freeze time and attack). Basically, you've been struck so fast that the attack literally took no time at all. Naturally, you can't defeat it until this ability has been nullified.
Word of God says that this holds true for the night sky in The Elder Scrolls. Mortals can't comprehend an infinite plane of existence enclosed in another infinite plane of existence which itself is enclosed in another infinite plane of existence so it all appears as a solar system.
This also applies to the eponymous scrolls, as what little you can see of the one you find before it blinds you for a few seconds is a set of strange runes and writing, when they're supposed to hold the world's entire history.
Including its future.
More comedically, the copy of Boethiah's Pillow Book found in the third game for the Thieve's Guild is implied to be so pornographic that "No words can describe what you see. Or what you think you see."
Devil May Cry 4 has Pandora's box, a Morph Weapon with 666 forms (not all useable), despite turning into a throwing glaive, a rocket launcher, or amissile platform its most damaging attack is simply letting the box drop open, revealing the contents inside to everything in front of Dante.
Final Fantasy VII has the ???? skill. That's right, even the name of the ability can't be determined. The effects of the spell is pretty nutty too as it only shows a weight with a question mark on it before dealing damage to the target.
Possibly due to the fact that it's hard to reduce its core concept to a few words; it deals damage equal to the amount of HP the character has lost in comparison to their max HP. "Revenge" was one name for the attack, but in Final Fantasy IX it was Played for Laughs, having the name "Pumpkin Head."
Eternal Darkness had a moment where Anthony, suspicious of the person telling him to deliver a scroll to Charlemagne the Frank, opens the scroll and catches a glimpse of a strange symbol before being Blown Across the Room by the power of the spell drawn on it.
Yami, the Big Bad of Ōkami is stated to be so alien an entity that it cannot be represented as either a human or animal. In actuality however, it takes the form of a mechanical sphere with a fish/fetus-like core.
Tohno Shiki of Tsukihime can see the 'death' of anything that has a flaw, but since human brains can't truly comprehend death as it applies to nonliving things, Shiki has to struggle to kill inanimate objects. He can even kill conceptual things like time or disease, although this places so much stress on his brain it nearly kills him. There are also beings who simply have no 'death', and thus cannot be killed, such as Arcueid during the night (which Shiki finds out to his chagrin during Ciel's route.)
Featherine Augustus Aurora from Umineko: When They Cry is an interesting take on this. While not really an Eldritch Abomination herself (we think), the form she assumes can vary. Being a witch of untold age, she had to create a horseshoe-shaped device that hovers around her head. This thing not only contains all of her memories, but even her physical appearance. According to Lambdadelta, it once got dinged in the past, abruptly changing Featherine's personality and form.
She can also use the power of You Cannot Grasp the True Form to initiate an attack in a similar vein to Giygas/Giegue. As the Witch of Theatregoing, she can literally stop time, rip out the script of a world and rewrite it. In the eighth and final book when she "fights" Lambdadelta, she starts from the end of the incoming fight scene and works her way back, only to the part where she deals a rather brutal finishing blow to Lambda. She doesn't even write what killed Lambda, deciding to think it up later. When time resumes, the poor Witch of Certainty suffered just as Featherine wrote and had no idea what just happened before perishing, the narrative almost quoting this trope word for word.
It gets better: Featherine isn't even the genuine article, but rather an Author Avatar of Ikuko Hachijō.
Bernkastel and Lambdadelta themselves might also qualify for this trope. The former is actually Ikuko's pet cat who takes the form of an older Rika Furude in the meta-world, and the latter is literally made out of candy.
The people at Nitro Plus made the brilliant decision in Saya no Uta to never actually show any clear shots of the monster(s). You only ever get to see individual limbs or extreme close-ups of certain body parts, with most of it being covered in darkness. What you get instead are detailed descriptions that paints mental images in your head. They realized that the true form of the monster would be more horrifying if the reader could only imagine it, and never actually see it. After all, to show the monster would mean that its looks were comprehensible. For it to be a true eldritch abomination however, it must be unimaginable.
Orion's Arm takes a slightly different approach. Understanding the mind of the archailects is impossible for a normal human. And actually understanding their physical form is pretty difficult too because they exist as multiple planet sized objects.
A good many SCPs are likely to qualify, although most are written as mundane things with strange properties, rather than strange things appearing as mundane things.
The most prominent of these would probably be SCP-055, which is a... thing. Anybody who sees it will completely forget about it within a few minutes. Anybody who hears or sees secondhand details, including picture and video, about it will also forget about those within a few minutes. The object is classified as Keter (most dangerous) simply because the Foundation doesn't know if it's dangerous, specifically mentioning that it could have killed hundreds of personnel in the process of getting it and they wouldn't remember any of it.
This story dials the horror of such a... thing that isn't spherical up to eleven.
In a Creepy Pasta called "The Cave", there is the Eldritch Abomination known as the Jackal. The closest to a description the narrator manages to provide when it is seen is that whereas its depiction had been scratched out from pictures on the walls before, looking at the real thing is a lot like looking at those pictures, because all you can see is still something blurry and formless.
The portals in The Salvation War are very hard for anyone to really comprehend what they are seeing, describing it in completely contradictory terms (for example, one character notes it looks both parallel and perpendicular to the ground). It is mentioned at it at least a seven dimensional object, and what is seen is a best the "shadow" of the real thing.
The Whateley Universe is simply packed to the brim with creatures whose true form cannot or should not be perceived by mortals. The character of Nacht gives an apt analogy:
Imagine that you’re in a boat and you see some fish in the water. You reach your hand into the water to grab one of the fish. From the fish’s point of view, this weird thing with a flat body and five tentacles and a weird thick tail that reaches out into nowhere, but no eyes, mouth or fins, just appeared in a shower of bubbles. It moves around in ways that have nothing to do with swishing its tail or moving fins in any way. Then this thing which shouldn’t be any stronger than the fish is, and has no eyes with which to see, wraps itself around one of the other fish, and suddenly that fish disappears from the first fish’s plane of reference. The hand is utterly alien to the fish, and it operates in ways that would seem magical to it, if fish had the brains to encompass the notion of magic. I think that your Headhunter is like that: it has much, but not all of the power of the demon at its disposal, and it has a perspective that most mortals can’t have, and it operates on very different principles and motives.
Robin from Teen Titans sees the entrance to the afterlife as a regular wooden door with LIFE AND DEATH written on it.
Which is taken directly out of one of the comics when Beast Boy and Raven venture there. They even make a remark about it;
Beast Boy: I can't believe the afterlife has a sense of humor.
Raven: Yes, it disturbs me as well.
In one episode of I Am Weasel, Weasel and Baboon use a bike so fast it exceeds the speed of light in which they find in Another Dimension where the living beings look like ham. I. R. Baboon tries to eat one even after the beings explain they aren't really ham, they simply appear as such to their minds.
One episode of Invader Zim parodies this with the Meekrob, who fly into Dib's room in the form of strange, glowing aliens, and then inexplicably transform into giant floating sneakers.
After getting crap for using A Form You Are Comfortable With, an alien on The Venture Bros. got mad enough to show them his real form. All the audience got to see was that it revealed itself by ripping its "face" open down the middle, had flashing lights, tentacles, and was enough to make a (mentally handicapped) character crap his pants.
The alien Vok in Beast Wars:Transformers capture Optimus Primal and communicate with him. But to do so, they first scan his memory banks for what he would consider a figure of authority —they choose to manifest as the disembodied head of Unicron. They're actually creepy glowing energy skull things that do very little.
Language is also linked to colors. If a language and culture has a bigger difference between colors, people in that society are better able to distinguish colors. This goes the other way too, as people who lack distinctions for colors are slower to recognize differences between them. However, the idea that they are incapable of doing so is pure myth; the difference is in fractions of a second of recognition speed, not actual differences in visual acuity. There is evidence that colors which humans cannot manufacture do not have names and are therefore not recognized. Scholars have studied ancient texts, including The Iliad and The Odyssey, specifically looking at the usage of color words. Many very strange color identifications are given: Green Honey, Violet Sheep, and Wine-Dark Seas. These were often regarded as "colorful" metaphors until linguist Guy Deutscher realized there is no blue. At the time there were no blue dyes available and there simply wasn't a word for blue, so people had to use other colors to describe what we now know as blue. This is a pattern across all cultures: color usage appears in stages, and blue is always last. This can also be seen in young children; if they don't yet know a color they'll refer to things of that color by a color they do know. An example, again involving blue, children will refer to the sky as white (which most adults will reflexively say is blue) before they know the color blue.
Some women have four sets of cone cells (the type of cell which is primarily responsible for our perception of color) in their eyes rather than three, which may give them a small advantage in distinguishing colors. People with only two sets of cone cells instead of three (color blindness) or with inadequate numbers of or malfunctioning cone cells (milder forms of color blindness) are less able to distinguish colors, and as a result colors which contain light of the wavelength they are "blind" to appear considerably different to them.
Probably related are images taken by telescopes (or other instruments, for the case) designed to work with wavelengths that do not correspond with visible light, like Spitzer (infrared) or Chandra (X-Ray). The images of Space Clouds that we see that have been taken by them are actually processed false-color images, so we can see them with our eyes and if they were sensible to those wavelengths while we'd see something more or less with the same aspect (ie: an infrared-bright region of star formation or an X-ray emitting gas cloud) , etc, their colors (to give that a name) would be quite different.
Human brains are designed to perceive the world in three dimensions, but the human eye only perceives the world in two dimensions. The brain uses the 2-dimensional input from each eye in addition to some image process recognition to construct the perception of a third dimension inside the brain, which is why people with only one eye have diminished depth perception. This can be thrown off in various well-known ways, such as presenting a different image to each eye - something 3D glasses take advantage of to create a stronger illusion of the third dimension from a 2D image. Many visual illusions take advantage of the brain's visual processing - perspective in paintings is a matter of tricking the eye into seeing 3D distance which is not actually present, while real-world environments can be constructed in order to trick the brain into seeing a 3D space as being larger, smaller, or otherwise strangely shaped.
Because the brain is designed to construct 3D images, it makes visualizing a object which has more than three spatial dimensions, such as some mathematical constructs, very strange - one of the more common ways of doing so is essentially taking 3-dimensional "slices" of a 4D object, and presenting them in series over time.
Blind spots. Your brain compensates for the existing blind spots in your eyes (spots which are not covered with cones or rods due to the presence of the optical nerve), filling in the lost information. People who get retinal burns (because of handling lasers or arc welders carelessly, for example) get additional blind spots in addition to the natural ones. The brain input-processing mechanism conceals these spots and the afflicted human thinks he's perfectly okay, up until the point that enough of his retina is burned that the brain is no longer able to compensate.
Because the brain is essentially a very complicated computer made out of meat, brain damage can severely mess up people's perception of reality.
A patient with the two hemispheres of their brain severed may be asked to pick up an object with one hand, pick up the object named, but then call the object by the wrong name when they are asked what object it is, or vice-versa. Such people may also only be able to solve math shown to one of their eyes; if it is shown to the wrong eye exclusively, they may not be able to properly solve the problem.
Left side paralysis caused by brain damage, not direct nerve damage, leads to the common illusion that the non-functioning body parts belong to somebody else. The reason is that since the damage originates from the brain, there is no feedback from the limbs to signal that something is wrong with them, since they are technically totally functional. Therefore, the brain invents the idea that the limbs must belong to somebody else. In cognitive science, this is referred to as confabulation. It is actually rather scary that a person under such an illusion is more or less incapable of understanding that they ARE, in fact, not right. They will acknowledge any arguments made by people trying to convince them, but they will not change their mind. When the brain no longer needs to delude itself, people are confused how they could have ever believed something so ridiculous. In some cases, the same defensive mental mechanism reoccurs, and people conveniently forget their previous puzzlement. And it should be noted, this happens in people who are otherwise perfectly reasonable, sane and rational, as far as it is possible to judge.
Synesthesia is another odd side effect of how brains function. Someone with synesthesia not only perceives the world in the same way that others do, but additional senses are stimulated as nerve signals cross over in the brain. Each synesthetic person has their own way in which their senses cross over; some see sounds, or hear colors, or feel colors. This is a very strange sort of qualia, and even two synesthetic people who share the same crossings-over may not perceive them in the same way.
Douglas Adams pointed out that infinity is flat and uninteresting, since it doesn't present magnitude or scale, ergo, really big things are necessary to show just how big it is. A basic example is the Googolplex, a number so large that it cannot be represented longhand, even if we filled the known universe with protons and wrote a zero on each one.
An even bigger number is Graham's number which cannot be expressed with any standard system of numerical representation including such things as exponent stacks (e.g. a^b^c^d^e...). However, like all things, it can be expressed using certain specialized forms of recursive notation.
Fun fact: Graham's number is the maximum limit of the number of unique variations of a particular problem. The minimal limit, at the time, was thought to be 6. (It has since been increased to 13.)
Numbers this large can't be constructed physically, and cannot be simulated on a 1 to 1 basis.
Infinity itself is difficult for most people to understand, and also has very strange consequences, as two infinite quantities are not necessarily equal, and some infinities are, effectively, bigger than others.
Related to this is infinitesimal, which is a something that can only be described as a value that is infinitely small, but still reasonably significant. It's probably first heard when taking a physics class or learning about integrals.
There are also an infinite number of numbers between 0 and 1, or indeed, between any two values.
Fractals. Their number of dimensions varies whether it's topological or not, and their "true" (Hausdorff) number of dimensions is often non-integer. The Menger sponge, for example, is an object which has zero volume and an infinite surface area. Which means that any Menger sponge you'll see is only an approximation.
For another example, look at Sierpinski's Triangles (imagine a Triforce where you replace every triangle with another Triforce ad infinitum). It has roughly 1.585 dimensions (more precisely, log(3)/log(2).
Averted in general with mathematics and geometry, however; while these things might be difficult to visualize, people with the right mathematical training are able to fully understand mathematical concepts on their own "true" terms without resorting to visual metaphors (in fact, learning to do this is essential to progress; not learning to do this is a large part of why some people find math hard).
This Crackedarticle contains some examples, particularly one mental disorder that makes it so you can only grasp the form of one thing at a time.
The philosophical concept of the Platonic Cave takes this on a cosmic level: the world we are seeing is just an imperfect illusion projected by metaphysical abstractions which are named by Plato as "the Forms" (whose true form we cannot see, hear or touch, only try to make sense and interpret through reasoning). This is related to the "magenta is not real" example above, in how the light and colours that we see are just abstract electromagnetic energy waves projected to our retina and interpreted by our brain as visual illusions. A common way to demonstrate this is the famous question: Sound waves, which we recognize as music or language, are in fact nothing more than molecular vibrations that are merely interpreted by the auditory nerve as "sound", so if a tree falls down and nobody can hear it does it make any "sound"?
That last example requires a bit more explanation. All "sound" is actually a wave of pressure traveling through a medium; in this case through air. According to the laws of physics a tree falling in the woods can, and indeed must, generate such a pressure wave, and thus make a sound, regardless of whether anyone or anything is nearby to hear it. The reason this trope applies is because the human brain can't actually perceive the pressure wave itself. It moves too quickly for us to observe in real-time. We can only sense the effect of the pressure wave when it hits us, which our brain reinterprets as a "sound". If we were able to see the vibration in real-time it would probably look something like waves on the ocean. Or like this Mythbusters clip.
Extremely distant objects in the sky are so far away that the brain does not naturally model them as being three-dimensional objects in space. This is especially true of the Sun, Moon, and stars, all of which are huge objects which are extremely large distances away, but the brain does not naturally perceive them as large, nor accurately model their distance, due to lack of perspective.
This is why the moon appears to be larger when it is low on the horizon versus up in the sky. There isn't an atmospheric lensing effect as many people believe, it's simple because there are trees/buildings/the ground now visible in proximity to it and your brain is better able to judge a relative size. Without the known size objects for your brain to compare it to it has no grasp for the scale.
Even non-celestial distant objects can mess with the brain's perception if there is no relative comparison. Just look at a plane in the sky, you have no way of judging how high or how fast it is moving other than "it's small so it's got to be pretty high". From the ground 2 planes (or their conning trails) could appear to intersect with each other and nearly collide, when in actuality there may be 2 miles or more difference in their altitudes. Without perspective the brain just gives up and renders it as a 2D image.
Your own incompetence. Competency in a task is linked to your ability to judge your ability at said task; thus, incompetent people, with no training in the task, will consider themselves to be vastly more competent than they actually are. This is known as the Dunning-Kruger effect; however, it can be mitigated with training. Unfortunately, the very incompetence of the people may prevent them from seeking out said training, because they don't realize how incompetent they actually are.
At the quantum level, electrons. To clarify, most subatomic particles exist as both matter and as waves including electrons. In fact the Heisenberg Uncertainty Principle essentially states that the more you know about one's position, the less you know about its speed or trajectory and visa versa. As such the very act of observing an electron is sufficient to alter either its relative position or trajectory.
Dark Matter/Energy. A postulated form of "something" that makes up over 90% of the universe but does not have any interaction with the electromagnetic spectrum. In fact the only "Observable" effect, and hint that it exists, is it's effect on gravity. Humans (and all life as we know it) is made of "normal" matter and evolved to perceive the world through a thin slice of the EM spectrum. Through technology we have been able to extend that thin slice to allow use to visualize other parts of the EM spectrum (which really makes another example of this trope: we cannot grasp the true form of any part of the EM spectrum except for the visible spectrum, only convert it into visual light which we are able to understand), but we are still limited to the parts of the universe that are also able to interact with the EM spectrum. Something that doesn't interact with it is therefore completely unimaginable.
All of Planck's constants are incomprehensible except one: Planck mass. The rest describe things like smallest unit of time or length to maximum temperature. Planck mass, while describing something on the quantum level, is the mass of a flea egg.