The So Bad, It's Good ads for Ginsu knives try to sell the Ginsu 2000 as an Absurdly Sharp Blade that Never Needs Sharpening. Though it's a Deceptively Simple Demonstration, as cutting through an aluminum can (or whatever absurdly hard object they demonstrate the knife slicing through) is a lot easier than many everyday cooking tasks, such as slicing through a winter squash, clearing beef gristle, or boning a fish fillet.
Chef Tony once advertised the Perfection Series knives as so sharp they can cut a pineapple in half in midair.
Anime And Manga
In Grenadier - The Smiling Senshi, the hero, a swordsman, has a(n impractically) long katana, sharp enough to slice an incoming artillery shell in half (without triggering the fuse), and cut a giant boulder clean in half, albeit with assistance from the heroine's pistol (four rounds to the back of the blade at the moment of contact, to propel it into the rock).
Goemon, from Lupin III, regularly slices through things like airplanes and buildings with his katana, the Zantetsuken ("Iron-Cutting Sword") — or in the manga, Nagareboshi ("Falling Star"). Episode Zero: First Contact and Dragon of Doom both explain that the Zantetsuken is made out of a mysterious alloy (in the manga, it's said to be made of a rare steel alloy produced from meteoric iron) that is almost indestructible, though apparently the metal can cut itself. Episode Zero finds Goemon wanting to destroy the formula for the alloy since he doesn't want to risk another Zantetsuken being made, rendering his own vulnerable.
Ax Crazy Sword Guy from the first episode of New Getter Robo has this going on with his katana. Including slicing down the better part of a Shinto Shrine. It works for Ryoma when he disarms him too; he grabs it, redirects into the face of one of his attackers, slashes the sword's owner with it, and then hurls it through the arm of the Knife Nut. There's a pause of about two seconds before his arm goes off and blood starts spewing everywhere. This fight was taken almost frame-for-frame from Ken Ishikawa's original Getter Robo manga, with the major exception that instead of Adult Ryoma, it was the classic version who did it.
Dragon Ball Z has Yajirobe's katana. Weapons are mostly useless against even weak enemies, but Yajirobe is able to accomplish feats like slicing off Oozaru Vegeta's gigantic tail in a single swing, despite his unimpressive strength (by DBZ standards).
Also Krillin's Ki-Enzan (energy disc), an absurdly sharp ki attack. Though Krillin himself is quickly Overshadowed by Awesome, his signature technique remains deadly, and at one point he is able to cut off Frieza's tail. His relative lack of power is an advantage with this technique: the disc is slow enough that most enemies see it coming and could dodge easily, but instead try to No Sell it, getting themselves cut.
Played with in Slayers with the Blast Sword. It was so sharp you couldn't put it in a sheath without cutting it in half. It was so sharp it was useless so they had to find someone to cast some magic on it to dull the blade. But even the dulled blade still fits this trope.
Parodied in Mahou Sensei Negima!, during a Yonkoma-styleOmake (seen in the 2nd anime ending: Setsuna sharpens a kitchen knife for Miu, which ends up cutting through the radish, cutting board, and about three feet of counter/cabinet.
Darker Than Black: If Hei's knives aren't these, then crappy concrete is probably more of a threat to Japan than Hell's Gate and everything that came out of it put together.
In Until Death Do Us Part, the protagonist's sword is camouflaged inside his white cane. Said sword is able to cut through a gun... And the cut is so clean they actually manage to stick the parts of the gun back together.
While Samurai Champloo contains more typical examples with swords, the blade on Umanosuke's kusarigama really takes the cake, being able to cut clear through rocks and thick wooden support beams without even slowing down. It also makes such an insanely loud noise when swung through the air that you'd think it's regularly breaking the sound barrier. Ultimately, this ends up completely biting him in the ass, as Mugen is able to swing the blade back at him and even without a huge amount of force behind it the thing manages to cut his head off.
Rurouni Kenshin is guilty of this. Sagara Sanosuke may have a BFS but Kenshin's original sword cut through it. He's also used the sharp side of his reverse-blade sword to slice through cannonballs and a huge lamp-post.
When his original reverse blade sword broke, he went to visit a swordmaker. That man's cutting knives (as in for cooking) were able to slice a turnip in half with a cut so fine that Kenshin was able to fit the two halves back together without showing a seam.
Mai in Kanon has a sword that's strong enough to slice clean through several metal objects around her and crush a brick wall.
The Blade of Masane Amaha's Witchblade in the anime, as demonstrated multiple times as it takes machines a while to realize that they have been cut and explode.
Every katana forged by Luke in The Sacred Blacksmith seems to be capable of cutting through most things, such as a two handed sword or another katana that was swung at it, meaning it can cut through other swords with no force behind it at all. His magically forged katanas are offset by their fragility, but they still cut through the insanely overpowered demon swords.
In his first episode on F-Zero: GP Legend, Samurai Goroh uses his sword to cut through prison bars, a missile flying towards him (while on the back of a moving vehicle), an armored vehicle, and at the end, an entire spaceship. Truly Goroh's blade is the mightiest force in the universe.
In Toriko, kitchen knives made by the master sharpener Melk can't be bought without a license, to prevent unskilled users from accidentally injuring themselves. This culminates in what could possibly be the best example of this trope, when Melk the 2nd completes Komatsu's new knife. A light swing of it proceeds to make a gigantic gash in the mountain. It didn't come in contact with anything.
In Berserk, Guts receives a sword from the master blacksmith Godo shortly after the Eclipse which proves itself capable of cleanly cutting through the blade of another sword and the tip of an anvil in a single stroke. However, an absurdly sharp sword of merely ordinary size doesn't suit Guts' style, and it doesn't last a single fight.
In Zoids, blades built into powerful zoids (particularly the Liger series) can cut through damn near anything, including blades used by Mecha-Mooks.
The swords given to the warriors in the unnamed organization in Claymore. This is lampshaded at one point when Miria says something along the lines of "Have you ever wondered why our swords never chip or dull, no matter how hard we swing or how hard the surface we hit? What exactly are they made of? The material can't be from this continent and I've looked everywhere."
The sword Melan wields in Brigadoon: Marin and Melan can cut through almost anything on earth, including bullets and gun barrels. However, it's not always successful against weapons made on Brigadoon.
If a monster in Yu-Gi-Oh! uses a sword, said monster has probably used it like this at least once, creating a Clean Cut in the opponent.
Micaiah's katana in Magical Girl Lyrical Nanoha Vivid, which is mentioned to be a normal physical sword. After she sharpened it for the tournament, she tests its edge by slicing a falling bus into fours.
The Gerbera Straight used by Lowe Guele's Gundam Astray Red Frame. He had it built because he needed a weapon to defend himself with, beam sabers drained precious energy and a GINN's Heavy Sword used inertia, thus precious energy, to cut.
Gundam 00 has the GN swords. They are all quite bulky, but they are absurdly sharp despite not looking like it. Justified in-universe as GN Particles can (apparently) be used to increase a solid blade's sharpness... whatever that means.
In Gintama, Sakata Gintoki's sword is so sharp it can be used to cut through several feet of metal. It's also made of wood.
Creed Diskenth's ki blade in Black Cat will slice cleanly through everything short of the orichalcum used in Chronos assassins' weapons. When he cuts off Train's hand during their first encounter in the manga, the doctor who reattaches said hand notes that it's as if the cells were simply pulled apart.
The mid-90s anime Chuuka Ichiban (Cooking Master Boy) has Leon, one of the main characters, in possession of a legendary set of seven cooking knives called the Seven Star Knives. The smallest is the size of a fruit knife while the largest is borderline BFS to prepare a cow or a bull. They're all so sharp that one of it was once used to cut open a fish's ovary, extract all the eggs, and then without any surgery, close the wound again due to the extremely clean cut it was made, and the fish is released back to water without so much of a scratch. This is consistent with the wielder's Actual Pacifist outlook, despite his Face of a Thug.
In Shingeki No Kyojin, the soldiers' specialized blades can slice into the giants' weak spots that even cannons have trouble destroying. The trade-off is they are so easy to dull and break, each soldier carries twelve of them and can still run out.
Wolverine from the X-Men has adamantium claws in his hands. There are very few things that they can't cut.
The Libra killer in Top 10 did this. In reality, she was an alien in a volatile life stage, with atom-slicing filaments coming from her body.
The Vorpal Blade wielded by Boy Blue in Fables. It's so sharp that the only time it didn't cut right through a target is because the target was the Big Bad, who has placed countless millions of protection spells on himself over the years.
In DC Comics, a sharpened blade coated with "lubrilon" is so slick it can cut through anything with almost no friction.
Vandal Savage's illegal Omicronian Knife Suit from DC One Million. It used nanomachines to constantly sharpen the blades so they could "cut out your very soul".
Sin City's Miho has blades that are sharp enough to slice right through human bone or, in one case, a car roof.
In World of Warcraft manga comics there is a tale of a dwarven blacksmith. He is regarded as the best weaponsmith in the world. After his son is killed by one of his weapons he forges the best weapon he has ever crafted for the purpose to avenge his son. To test his blade he he destroys his own anvil with a single one-handed strike.
In the Kung Fu Panda story Making the Cut, Jo is able to cut a single strand of hair by dropping it onto the edge of his obsidian dagger.
Something of an Informed Attribute of the Lotus Blade in the Blood Bond, Blood Omen Series of Kim Possible fanfics. While it can obviously take any form that Ron likes while he's wielding it, when Kim AKA the Scarred Warrior wields it, it becomes simply a "very hard, very sharp" sword, one "so perfect that – if one of the men of the school had been so blasphemous as to try – it could easily be shaved with." And this description comes from Sensei, who has surely seen his share of swords. On the other hand, we never see it cut anything that an ordinary sword couldn't cut, at least not when it's in sword form.
Sephiroth receives a magical dagger that can cut through any substance as a present from Yuffie in Shinra High SOLDIER.
The Hattori Hanzo katana owned by the Bride in Kill Bill. "I can tell you with no ego, this is my finest sword. If on your journey, you should encounter God, God will be cut." This is a quote of Musashi, although in his context it meant steeling yourself for battle no matter who faced you.
Shortly after Logan receives his adamantium infusion in X-Men Origins: Wolverine, he slices up several items in a farmhouse bathroom (including a porcelain sink) with his now impossibly sharp claws, despite applying what appears to be no more than the force required to move an unrestrained arm.
The legendary Green Destiny sword in Crouching Tiger, Hidden Dragon is capable of slicing through virtually any other weapon, and apparently never gets chipped or cracked, regardless of how often it gets used. Amusingly, in one of the later fight scenes there is a blink-and-you'll-miss-it shot that clearly shows the prop sword to have been severely deformed in the action sequence.
In Clash of the Titans, Perseus receives a sword from the gods that slices through a block of marble without leaving a scratch on the blade. This is the weapon that he later uses to slay Calibos. And he wasn't even trying to cut the marble, he was just a bit careless with how he lowered the sword after testing the balance and accidentally hit the marble block.
At one point in The Forbidden Kingdom, the blade of the Jade Warlord's weapon is smashed into the floor, and then dragged across the room. It cuts through the stone floor like butter. Granted, this is probably a magical blade, but still.
Machetes in Walk Hard. They have to be sharp to cut a person in half and impressively sharp to do so on accident, but it's reaching into the realm of the absurdly sharp when you can cut yourself in half by accident.
A scene in The Bodyguard involves a katana and a silk scarf. The scarf falls across the katana's blade and is sliced in half by its own weight.
Hilariously inverted in Hot Shots!: Part Deux; Topper swings a sword through a candle, and it passes clean through... only for the sword to break a moment later.
Ninja Assassin has this on every blade we ever get to see. The swords can cut a man in half, and on one occasion, the protagonist is seen slicing open a wooden floor with his kusarigama. The shuriken are also pretty sharp, able to slice a man's head in half or cut off two arms at once, without changing trajectory. The movie actually spends a lot of scenes showing ninja sharpening their blades.
In Kick-Ass, Hit-Girl (a 10-year-old girl) uses a double-bladed weapon to cleanly and casually slice the leg off one opponent, then stabs her blades through a metal door.
Dragonslayer. Galen's lance, which is aided by a magic fire to make it sharper than sharp. It slices through the anvil with little effort.
In ZatoichiLong Runner, Ichi's sword cane (shikomizue) cut through candles, papers, lanterns, shōji's (doors, windows), ryō's (golden coins), wooden buckets, wooden columns, pushcarts, stone statue and katanas.
Kung Fu Panda featured the Sword of Heroes. "Said to be so sharp you can get cut just by looking at — Ow!"
Both the scythe and the sword of Death , especially in Hogfather. The edges of these weapons glow blue because of the air molecules being sliced in half all the time. The sharpness even extends a few inches beyond the blade due to the impossible aura of sharpness. In Reaper Man, Death sharpens his scythe on sunlight, and then tests it by cutting a sentence Miss Flitworth is speaking into its individual words.
Death defeats his evil replacement with an ordinary field scythe sharpened by his own pure rage. Rage isn't even "real," like light, it's just an abstract concept.
Carrot's sword is sharp enough to pierce a solid stone pillar. It is the long-lost sword of the Kings of Ankh, and the Disc's rules of Narrative Causality insist that such a historic weapon must be sharp enough to do such things. His ancestors specifically didn't want a magical sword; they wanted a sword that was really good at killing people.
In Interesting Times, when a small army of samurai demonstrate their absurdly sharp blades by throwing silk cloths in the air and slicing them in two, a reference to the old Saladin/Richard legend. Combat Pragmatist Cohen the Barbarian claims he can do the same with his ancient notched sword — then, while they're all looking up at the handkerchief, he and his men decapitate nine of them. In The Last Hero, however, Cohen uses the same sword to roll a seven with a six-sided die by slicing the die in half while it's in the air, so his sword must be quite sharp.
"Every established kitchen has one ancient knife, its handle worn thin, its blade curved like a banana, and so inexplicably sharp that reaching into the drawer at night is like bobbing for apples in a piranha tank."
Subverted in the The Dresden Files. Throughout the series, you see the Warden's specially enchanted swords, which cut through demons, summoned constructs, and enchantments with ease. But Word Of God explains that while these swords are indeed magical, their sharpness is simply due to them being really well-made swords.
Played straight with the Knights of the Cross' holy blades. One cut right through a steel door.
One of the evil empire's primary advantages in the Farsala Trilogy is that their folded steel blades ('watersteel') can cut through the Farsalan weapons, though with their superior numbers, much smaller egos, and much greater brains than the first line of Farsalan defenders they hardly need them.
In the Cross Time Engineer novels, Conrad Stargard has a sword that regularly slices through armor, body parts, anvils, and other swords. He thinks it is just really good steel. In reality, it has a diamond edge and was made by the same highly advanced people who accidentally sent him to the 13th century.
In the Sten novels by Allan Cole and Chris Bunch, the signature weapon of the eponymous hero is an absurdly sharp knife that can cut almost everything, even diamonds. And he keeps it hidden inside his arm.
In The Princess Series, Danielle Whiteshore- Cinderella- possesses an enchanted glass sword as the final gift from her mother's spirit, capable of cutting through anything apart from Danielle's own flesh.
In his World's End series, Lin Carter uses a super sharp sword, in Ganelon Silvermane's "Silver Sword", although it won't quite cut anything — there are limits, it seems.
In The Silmarillion, the knife Angrist, a knife that can "cleave iron like green wood..."
In Lord of the Rings elven blades are sharper than anyone else's and the blades hold their edge forever. Then there's the dwarven-made Narsil, which is absurdly sharp even by elven standards.
Blades of Valyrian steel are far sharper and stronger than even the best mundane steel. Forging the metal is a magical process that has become Lost Technology after the fall of Valyria. It has a smoky, rippled appearance that resembles Damascus Steel.
Dawn, the ancestral blade of House Dayne. The blade was forged from meteoric iron and is hinted to be of extraordinary quality. Arthur Dayne, the Sword in the Morning, notably used it to hack a foe's sword to bits, then chivalrously allowing him to retrieve another sword before slaying him. Jaime Lannister also recalls that the sword cut through his tunic and into the flesh beneath when Dayne tapped it against his shoulder to knight him.
In Everworld, Coo-Hatch steel is used to make absurdly sharp blades. The Coo-Hatch show off by cutting a tree into pieces, which stand for several seconds before falling, and then cutting the falling pieces with throwing blades. Later, a Coo-Hatch pocketknife is used to tunnel through rock. Very slowly.
In The Inheritance Cycle, Angela the Herbalist has a sword she calls "Tinkledeath" which is so sharp that it can literally cut through anything as if it were custard. Throughout the series, all Riders' swords are imbued magically such that they never rust or dull and can defeat or outright ignore most enchantments. They're also forged using a rare meteorite that the sword smith Rheunon named "Brightsteel" which has a notable crystalline structure. The same is true of Eragon's first Riders' sword, Zar'roc. After getting a new sword in Brisingr, Eragon was able to cut through a portcullis and then the door behind it.
The contemporary fantasy novel Into the Out Of by Alan Dean Foster features an African master woodcarver who furnishes the heroes with wooden knives and spears so sharp they give you a paper-cut like cut just from touching the edges of the blades and can be thrown right through a wall. You can't even quite make out where the edge of one of them ends and the air begins, they're so sharp. As one of the characters describes them:
"They are wood, but they are anything but ordinary. There are no other such weapons anywhere in the world. They are blackwood plus history, blackwood plus a little of every weapon that has ever been. There are the spears of the great Zulu impis in each edge, the power of Tamerlane's hordes, the thrust of Caesar's legions. On the very edge of each swim things that race the components of existence around racetracks on which the beginning and end of the universe is the bet. They contain weapons that have not been and weapons that will never be. They are blackwood plus all that plus Nafasi. Into them he has put his heart and soul and much more. They will cut well. I think they will even cut a shetani."
In one of the Left Behind novels, Carpathia is slain with a sword that's supposedly sharp enough to sever half of someone's fingers off, before they even notice they're being cut.
The Wheel of Time series brings us Power-wrought blades. They can cleave through metal armor and the tough flesh of a Trolloc with limited resistance. Lan notes that they never need to be sharpened though some men have been known to try, resulting in wearing a whetstone to nothing for no good reason.
Flann O'Brien's The Third Policeman features a spear so sharp that if you were to prick yourself with it, your finger would begin to bleed about two inches before the point appeared to reach your finger. In fact, when your finger starts to bleed, the spear point had penetrated your skin two inches ago, but was so thin it slipped between the atoms of your finger without causing any damage.
Animorphs has Andalite tail blades that seem to be able to cut through pretty much anything. Although, at one point, Tobias (in Anadalite morph) gets his tail blade stuck in the trunk of a tree he was practicing on, much to Ax's amusement.
The main character of the Safehold series has one of these, it's made of some super-hi-tech alloy that's nearly indestructible to boot, he actually considered making an even sharper blade with an edge Sharpened to a Single Atom, but decided that was overkill. It helps that the character in question is a Ridiculously Human Robot with Super Strength who can thus put enough force behind the blade to slice an opponent's own sword into bits. Later he gives another character a similar blade.
There's one of these in The Magic and the Healing by Nick O'Donohoe.
The The Devil's Dictionary's article on Scimitars has a lengthy passage on an executor flourishing his sword before lightly tapping the condemned man's neck. He is later called in to explain why he didn't kill the man, and realized he had in fact decapitated himself while showing off.
Shardblades in The Stormlight Archive are an interesting variation. They are explicitly magical weapons, and can slice through any nonmagical material — stone, metal, etc — without slowing. They only things they don't cut are other Shardblades, Shardplate, and living flesh. The latter the blade simply passes through without marking, and "kills" the part of the body it passes through, as if severing nerves without touching anything else. If it passes through any part of the spinal cord the victim dies instantly, and their eyes burn out. It's implied that the blade in fact cuts the soul.
His Dark Materials: the Subtle Knife. Pretty clearly demonstrated throughout the story that it can cut through anything like butter. Including the boundaries between dimensions. Once it was dropped blade-first into stone: it didn't even slow down until the hilt hit the ground, after blade had already completely sunk.
In an episode of Mister Rogers' Neighborhood, Jay O'Callahan told the story "The Bubble", about a king stuck in a giant bubble and his attempts to get out. One of the knights who failed to pierce the bubble had a sword so sharp it "cut the wind and made it bleed".
Parodied in an episode of Newsradio Matthew gives Bill a katana which Bill thinks is fake. When Bill realises it's real he drops it and it cleanly cuts off a piece of a nearby table as it falls.
The 1998 television series Merlin has an example of Excalibur that fits this interpretation. Just parrying a weaker sword will cut the weaker sword in half.
In Teen Wolf, werewolf claws, despite looking almost like 'normal' sharpened human nails, can substitute a knife to cut cable and rake through metal effortlessly.
An episode of Warehouse 13 revolved around the threat of the assembly of the Masamune. The sword was so sharp, it could cut through light, rendering the user invisible. That was clearly a bit of hyperbole though, since that function didn't work until the tsuba (the little circle thing above the hilt) was reattached. That said, the sword is absurdly sharp in its own right, as it was able to slice through a computer monitor effortlessly.
In an episode of Castle ("Heroes & Villains", s4e2), a victim is laterally bisected apparently through his skull by what turns out to be a samurai sword.
Pretty much every Highlander episode with a beheading... most swords, with the possible exception of a katana, can't sever a human head in one stroke.
One of the Salamanca cousins in Breaking Bad carries a chromed fire axe. It's sharp enough to stick in pavement just from being accidentally dropped.
Myth & Legend
Some incarnations of King Arthur's sword Excalibur fit this trope. Depending on which legend you're reading (and which interpretation of the legend), Excalibur is either the most powerful blade ever worn by a British king, or else was just a sword. Many linguists believe that "Caliburn" (which became Excalibur) is an Anglified spelling of a Welsh phrase meaning Cutsteel.
In Norse Mythology, the Dwarf-forged magic sword Tyrfing could cut through metal and stone as if they were cloth. Needless to say, it could wreak havoc on an opponent's armor and weapons (to say nothing of the opponent themselves). Especially since it was never supposed to miss.
The ability of a sword to shave hairs was impressive because of the sheer thickness of the blade (and thus the trouble of getting a very sharp edge without burrs). Some swords of antiquity were in excess of 1/4" thick. Having a sword capable of field combat yet also able to shave hairs was a sign of superior bladesmithing.
There are claims that certain units of lancers from Eastern Europe and Eurasia (it has been attributed to Polish lancers and Cossacks) would shave with the tips of their lances before battle, and if their commander could see any stubble or nicks on their chin, then their weapons weren't sharp enough for battle.
A popular Japanese legend tells of a competition between two famous swordsmiths: brilliant but slightly unbalanced Muramasa Sengo, and even more brilliant and universally revered Masamune. Each smith held his sword tip-first into a gentle brook, with the edge facing upstream. As leaves floated down on the current, Muramasa's sword cut them neatly in half as they wafted against the blade. Leaves that encountered Masamune's sword, however, would make a 90-degree turn and avoid the blade altogether, in a Crowning Moment of Zen. In other versions of the legend, the leaves that Muramasa's blade cut, Masamune's blade healed together. In yet other versions the blades were placed in the river and floated downstream. Muramasa then argued that his blade was finer since it cut the leaves, Masamune pointing out that such a blade was inherently evil and bloodthirsty, which his wasn't, therefore was superior.
In American tall tales, Pecos Bill's razor was so sharp he shaved with just the shadow of it! (Which means he didn't shave so well on cloudy days, when the shadow was dimmer and fuzzier.)
The Germanic tale of Wayland/Velent/Völund/whatever has the hero make a sword, Mimung, so sharp that he slices the competing smith Amilias from the head down in half with one stroke, complete with his extremely thick armor, and Amilias didn't discover this until he was asked to shake, at which point he fell apart.
There's an apocryphal legend about Richard the Lionhearted having a conversation with Saladin about their respective swords. Richard requests an iron bar, and chops through it cleanly. Saladin shrugs, and requests a silk pillow. Richard's sword fails to even mar it, while Saladin's scimitar slices it neatly in half. More fanciful versions of the story have Saladin letting a silk veil fall across the edge of his scimitar, and cutting itself in half, while Richard was able to split an anvil.
A 20th-century apocryphal tale has a burly Afrika Korps infantryman going hand-to-hand with a Gurkha. The latter delivers a throat-high slash with his kukri, which the German doesn't even feel. "You missed!" he snarls, preparing to skewer the little Nepalese guy with his bayonet. Unperturbed, the Gurkha just says "Nod your head...". And, of course...
Islamic folklore has Zulfiqar, Ali's sword. It was found by Muhammad in the Mecca temple of Ishtar, and described as a long scimitar with a curious forked end. According to the legend, the archangel Gabriel constantly chained the true power of Zulfiqar since it was so sharp that at full force it could create Kamaitachi that would cut mountains apart. Another myth says that Ali killed an enemy knight by beheading the horse and slicing the knight in half with a single slash.
According to the Norse/Germanic saga of Sigurd/Siegfried, same hero's sword Gram/Balmung/Nothung was so sharp that he tested it by slicing an anvil in half.
Warhammer Fantasy has the Runefangs, dwarven-made swords that are wickedly sharp. There are twelve of them, each made for one of the Elector-Counts of the Empire. None of the people the swords were made for lived long enough to use them, because the dwarves wanted them to be perfect and it took longer than a human lifetime for the smith to make them all. The descendants of the original intended owners use them just fine.
Warhammer Fantasy Roleplay allows runesmiths to create more Runefangs by adding the master rune of Alaric the Mad (the smith of the original Runefangs) to weapons. Lest you think this a Game Breaker, creating a new Runefang can only be done by a master runesmith (a tertiary career), will take years for a Player Character even without failing any checks (making a sword that can become an absurdly sharp blade for a single blow is easier, taking a few days' off-time), and it's explicitly verboten for a runesmith to ever create two weapons with identical runes on them (that Alaric did this is why he's called 'the Mad'), and master runes occupy all slots on a weapon.
Weapons made of adamantine bypass most objects' hardness — meaning that, essentially, they're so sharp that they can cut steel (hardness 10) as easily as paper or cloth (hardness zero). Of course, this ability only works on objects up to hardness 20, meaning that adamantine (hardness 20) cannot cut itself.
The major artifact sword Angelwing Razor is so sharp, it can cut through literally anything, bypassing all forms of hardness and damage reduction. this includes barriers of pure magic that have no actual material substance.
The Everway RPG had among its legendary artifacts a sword named the "The Edge of Light and Darkness", which was created to exemplify "the dividing line between Is and Is Not". The Edge of Light and Darkness could cut anything its owner could conceive of cutting, and could wield the blade with sufficient skill to hit. In addition to the relatively mundane task of doing a Clean Cut through any physical substance, known examples include cutting through the fabric of space-time to create portals between alternate universes, killing an opponent by cutting his soul free of his body (without actually leaving any physical wounds on his body), and destroying a pocket universe by slicing the substance of reality into its fundamental elemental components.
7th Sea has the crescent-shaped scythe of the NPC Captain Reis, which allows him to cut through anything — even armor made from Dracheneisen, the 7th Sea version of Mithril, gets cut in half like so much butter.
New World of Darkness has a supplement called Dudes of Legend: How To Be Fucking Awesome. It contained- among rules for using your genitalia as a bludgeoning weapon, instituting experience charts for kills and other things that ran completely contrary to the intended feeling of nWoD- a hack that let you wield a katana that had the 7-Again quality, allowing you to reroll any result of 7 or higher on a d10. Considering that the system only counts successes at 8 or higher, and rerolls at 10, you will reroll every success you manage to get, again and again. It's explicitly intended to simulate these kinds of weapons.
GURPS Ultratech has a number of (increasingly super-science) ways of justifying this. Superfine blades divide damage resistance by two. Monowire and nanothorn blades divide damage resistance by ten, and the latter is additionally described as shredding molecular bonds.
In Exalted, assorted magic allows blades to cut through everything, up to and including spirits, mountains, memories, souls and reality, amongst other things.
Based on stories similar to those in the Myths and Legends section, above, Richard Wagner in his music-drama Siegfried, has the eponymous hero, after he has reforged his father's sword Nothung, use it to slice in two the anvil he has formed it on.
Devil May Cry displays this trope every time a sword is used in a cutscene. Word Of God says that Dante's blade is capable of slicing absolutely anything in the physical plane. Not very convincing after the series' later graphical pushes (the rust and nicks become more pronounced).
The Rebellion is upstaged by that of the Yamato, Vergil's trademark sword, which is capable of cutting through dimensions.
Darkstalkers has Bishamon's ancient blade, Kien. The sword was originally forged because talented warriors were frustrated that their swords had dulled irreparably. Thus Kien was crafted — using forbidden techniques — in such a way that it actually became sharper the more it was used, meaning a stronger blade from multiple battles. However, Kien eventually fell into the presence of the demonic Hannya, "the armour of hate", and was subsequently corrupted, gaining a thirst for blood...
In Final Fantasy VII Sephiroth's Masamune: in one scene in Crisis Core where he's fighting Angeal and Genesis, Sephiroth tears apart a gigantic cannon with it by slicing through the barrel with Sword Lines from the blade during the fight. That's one bad-ass sword.
Odin's One-Hit Kill attack cuts (Zantetsuken) all monsters on the battlefield in half.
Which caused the Zantetsuken to go spinning off into the sky, cutting a hole clean into another dimension. Specifically, the Interdimensional Rift from Final Fantasy V, where it was caught by Gilgamesh.
In Final Fantasy VII: Advent Children/Complete, Sephiroth's Masamune and Cloud's Fusion Swords are capable of not only slashing cleanly through massive pieces of concrete buildings that are far larger than the swords themselves (which is saying something), but setting the edges of the cut concrete on fire. Of course, the swords, despite repeated clashing, never damage each other.
Samurai Shodown II features Cham Cham, resident Cat Girl with her Improbable Weapon, a wooden boomerang used for melee combat. It's considered sharp by the game, enough that (in the original releases) you could trigger the game's Diagonal Cut death animations if you ended a match with a strike from it. Or if you pitched it at an enemy. Her claws work the same, too. 'Oh! How dangerous a boomerang is!'
In Super Robot Wars, there is nothing that Sanger Zonvolt's Zankantou/Colossal Blade cannot cut. It achieves this by having thrusters on the non-bladed side, allowing it to keep cutting even when it should get lodged into its target. This allows it to cut through huge battleships, hence the name "Zankantou", but it still breaks when it tries to cut into Giganscudo's Unobtainium armor. The Type 3 blade, however, is made of liquid metal and Runs on Badassoleum, making it more an example of this trope.
Youmu's sword from Touhou. "The things that can't be cut by my Roukan Blade, forged by Youkai, are close to none!" It is able to cut spirits and possibly other intangible things. However, her other sword, Hakurouken, while not as absurdly sharp it has the power to cut confusion, to the point of potentially giving instant enlightenment to spirits. It however still hurts humans.
In Nethack, the Tsurugi of Muramasa and Vorpal Blade each have a 5% chance of bisecting (in the case of the former) or decapitating (in the case of the latter) what they hit, causing instant death.
In Chrono Trigger, once repaired, the Masamune sunders a passageway into a mountain.
In Skies Of Arcadia, Ramirez's sword is described as being sharp enough to cut through light (which appears to be evidenced by his powerful "Silver Eclipse" attack).
Rayne's wrist blades in Blood Rayne cut through bone as easily as air. Also wood, stone, many kinds of metal — anything that can be demolished in the environment she can put a blade through as easily as waving her hands.
Fallout New Vegas - Dead Money: The Sierra Madre Casino's kitchen staff believed that the Cosmic knives they were supplied were too sharp for their needs. Sure, they could slice through a T-bone steak with no problem, but they'd cut through their cutting boards and their own fingers just as easily.
Geralt of Rivia's swords in The Witcher are described as being absurdly sharp. Later on in the game if the player kills Vincent. The Guards originally believe only a Scythe would have been sharp enough to kill him.
Baldur's Gate II has the Silver Sword, which is a vorpal blade as outlined under the Dungeons & Dragons rules above. It has a 25% chance to instantly kill anything it hits. (Although most bosses are immune.) The Expansion Pack added the Axe of the Unyielding and the Ravager halberd which have a similar chance for an instant kill.
Baninja's "katanana" in Banananana Ninja is a tiny sword wielded by a banana, which can cut through the roof of a bus and cleave through Humongous Mecha. He stores it in his head, disguised as his stem.
In Red vs. Blue Revelation, Tex's combat knife is sharp enough to pierce the meta's armor when Washington throws it.
In The Dreadful, during a non-canon advertising intermission, heroine Kit is depicted effortlessly slashing villainous monkeys to bits with a sword that is apparently made from a single large feather.
In Gunnerkrigg Court the sword that Coyote's fang is so sharp that, not only can it cut through an iron girder like butter, and cut a steel ball bearing in half just from being dropped against it's edge, but it also effortlessly cuts Robot's body in half and peels a shadow up from the floor. Oh, and said edge rings with Coyote's laughter.
Black Knight in Marvels RPG wields Excalibur, which is so insanely sharp that he can cut through anything... and then comes all of its magic abilities.
Chapel manages to decapitate Porter with a sword she bought...at Ren Faire.
From the Global Guardians PBEM Universe: A Espada ("The Sword") is a Brazilian who can create a "sword" out of pure mental force that can cut through anything as long as he has confidence that it will. Pendragon, a British hero, wields the legendary sword Excalibur, and has yet to meet a substance it cannot hack through. Fey, a mystic swords man who claims to be from the elf-lands of Faerie, once used his sword to cut through a bank vault door, though he says it's all in the magic and not in the blade.
The Whateley Universe stories have a few of these. The magical sword Destiny's Wave, wielded by The Handmaid Of The Tao (a superheroine codenamed Bladedancer). In the hands of the rightful user, it can cut through anything (even unstoppable superhuman bricks), if the Tao requires it. At other times, it is as blunt and harmless as you'd expect of a blade made of white jade. And then there's Toni's mithril Kukri, Fey's scimitar Malachim's Feather, and Hank's PK shortswords.
Dominic's sword in Ather City. Don't bother asking which one, because it seems to spontaneously apply to every sword he picks up.
SCP-585 is a pencil sharpener which infinitely sharpens the points of graphite pencils. To the point of their being able to penetrate steel. And bedrock. And split atoms.
Armsmaster, a tinker/martial artist superhero in Worm, developed a halberd with a nano-cloud blade that can turn anything to dust. He does more damage to Leviathan with it than the rest of the heroes and villains put together.
Samurai Jack's ancestral sword fits this bill very well. It can potentially cut through almost anything, but he has came across things that he simply wasn't strong enough to cut. It was a plot point at one time, when Jack had to destroy a series of robots Aku supercharged himself - the blade couldn't cut, because Jack wasn't strong enough, but when given a bionic arm by the creator of the robots (who was tricked into making said robots for Aku), he's able to decapitate them easily.
There was also a rather entertaining episode in which he proved that the sword wasn't everything — he took on an entire army of Mecha-Mooks with a bamboo stick. And cut them in half with it.
The Scotsman's magical Claymore, being just as powerful as Jack's katana and capable of wounding Aku, averts the idea that Katanas Are Just Better.
Avatar The Last Airbender has Sokka's "space sword". Its sharpness doesn't come up that often, but during the invasion, he cuts through a ballista in one swing. In the finale, to stop fire benders, he throws the sword and even without any weight backing it up, it cleanly slices through a sturdy metal platform. Moments before that, it also works against him, when his attempt to stop a fall by stabbing the hull of the airship just results in the sword shearing through the metal until they reach the bottom and keep falling.
Much earlier in the series, in "The Blue Spirit," the titular masked spirit uses dual Dao sabres to cut right through the chains holding Aang captive. In a single stroke.
In one episode of G.I. Joe, Cobra swordsman Storm Shadow gets his hands on the original Excalibur, which among other things can cut right through an enormous stone pillar with one swipe.
Near the climax of The Hunchback of Notre Dame, Frollo pursues Quasimodo and Esmeralda on the balcony of Notre Dame, all the while cleanly slicing through stone gargoyles attempting to slash at them.
Related to this trope is the old cartoon gag of a blade being sharp enough to split a hair neatly in two. A notable example is in the Looney Tunes short "Ali Baba Bunny", where Hassan's scimitar comes short of piercing Daffy's skull but it does part a single hair (feather?) on the top of his head.
In the Adventure Time "Slow Love", Jake and Finn's tree house gets dragged around by a giant snail. At one point it cuts to the bedroom, showing Finn's sword falling over and completely slicing through his bed.
Finn's Root Sword cuts through a train's control panel when it's first introduced in "Mystery Train", and yet Jake is able to block it with a wooden sword.
Played With in the ThunderCats (2011) episode "The Duelist and the Drifter" where several swordsmen in an Adventure TownInvoke this in the local sword competition, each bragging of their blade and striking a towering, giant boulder to see how deeply it cuts (one prideful Pig Man sees his sword shatter on impact.) Only young hero Lion-O makes good on his boast, as his Sword of Omens totally cleaves the boulder in two with a classic Diagonal Cut, winning him a hefty purse.
The Star Saber in Transformers Prime can cut through an entire mountain with little effort (as can its evil counterpart, the Dark Star Saber). Part of that, though, is the large sheets of Hard Light it shoots, rather than its actual cutting edges (not that it isn't Absurdly Sharp).
To prepare a slide for a transmission electron microscope, a diamond blade is used to get a less-than-paper-thin slice. Once properly sharpened, it's about a hundred atoms wide or so, and it will slide through your hand as easily as through the air.
There is another type of blade used in microtomes to prepare samples for the electron microscope: Freshly broken glass. A fresh one is among the sharpest cutting instruments known to human science.
Knapped obsidian blades are a small and measurable number of molecules in thickness. And while diamond is the harder material, obsidian can be made sharper. The greatest of care should be used in handling obsidian knives and arrow points, etc. because they can remain truly Absurdly Sharp even centuries after being made and will cut you badly with even the slightest touch. The drawback of course is that being basically an exotic form of glass, they wear out quickly in use.
Obsidian blades are still used in eye surgery when a clean cut is needed.
Anthropologists and paleontologists have "tested" the technology available to Stone Age humans by using hand-knapped obsidian blades to butcher an elephant's carcass.
The Aztecs used obsidian blades embedded in a wooden club to make a deadly weapon known as the Macuahuitl. The blades were easily sharp enough to decapitate a man, and can supposedly decapitate a horse if used correctly. (Unfortunately for the Aztecs, a glass blade, no matter how sharp, isn't durable enough to be much help against an enemy armored in steel.)
Traditionally, the balisong was tested before it was sold. The vendor would take out a few one-peso coins and stab right through them with the blade. The blade would be completely undamaged, and the coins (and table) would have holes in them.
This worked only because the coin was nearly pure silver, as opposed to the 925/1000 silver in jewels. Silver is very soft, Mohs hardness of about 2.5, and can be scratched by a human fingernail. Think modern electronics solder, with lead replaced by silver in the alloy, and even this is harder than pure silver.
A similar tale is told of the original Bowie knives. Their maker supposedly tested them by whittling a piece of hickory for a couple of hours, after which the knives still had to be sharp enough to shave a man's arm without nicking him.
This is less fanciful than it may appear. The original Bowie knife (made for Colonel Bowie himself) was forged from a large file. Files are made of extremely hard steel (so that they can be used on regular grades of steel), so as long as it was properly tempered the blade would hold an extreme edge through treatment like whittling.
Some modern steels such as CPM-154 can be taken to this point by a user skilled at sharpening with fine grit stones or strops. Depending on the steel, this edge can last for a while before use dulls it down.