All that is written, all that never was, and all that ever might be.
Everything would be in its blind volumes. Everything: the detailed history of the future, Aeschylus' The Egyptians, the exact number of times that the waters of the Ganges have reflected the flight of a falcon, the secret and true nature of Rome, the encyclopedia Novalis would have constructed, my dreams and half-dreams at dawn on August 14, 1934, the proof of Pierre Fermat's theorem, the unwritten chapters of Edwin Drood, those same chapters translated into the language spoken by the Garamantes, the paradoxes Berkeley invented concerning Time but didn't publish, Urizen's books of iron, the premature epiphanies of Stephen Dedalus, which would be meaningless before a cycle of a thousand years, the Gnostic Gospel of Basilides, the song the sirens sang, the complete catalog of the Library, the proof of the inaccuracy of that catalog.
A library that contains practically any possible/concievable information source known to man (or some other intelligent/sapient species), if not a multitude of intelligent species note or seems to, at the very least, in which case the subversion of expectations would cause in-universe shock/disbelief). This labyrinthian library seems to be a natural breeding spot for MacGuffins and it has just about all of life's secrets and answers. The Great Big Book of Everything,note Try not to think about whether or not that book would contain a copy of every book in the library, including itself. Seriously,don't.Big Book of War, Reality Writing Book, Portal Book, and chronoscopes along with other things can all be found here. Because of its wealth of knowledge, the library is a very valuable information resource for the main cast. May be a Magical Library as well, which could go a long way into justifying its often unreal/absurd level of comprehensiveness.
Often times this is guarded by a Magic Librarian or other force. Sometimes there will be a struggle with another group trying to obtain the same information, sometimes in a physical fight, but just as often with a Battle of Wits. If you're lucky, you'll find what you need. If you're not, it may turn out to be a Blank Book all along.
In many works, this setting is either very hard to get to, long forgotten, or rumoured to be a myth. In sci-fi and High Fantasy works, however, the library can be quite well publicized, and it's sometimes a big tourist destination.
Please note that the library must not be split up into multiple smaller libraries but instead be a continuous entity. So you can have a huge connected library, but not a bunch of smaller branches.
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The Infinity Library of the Lyrical Nanoha francise has all the publications and data of every world, and has been described as containing the memories of the universe. It's so huge that nobody has cataloged even a small fraction of it, and people wanting to use it for research often form multi-week expeditions to do so. These are people who can use search magic to speed things up and read several books at once, mind you.
Mahou Sensei Negima! has Library Island, a city-sized underground library so massive that Mahora actually has a school club dedicated to exploring it, with standard club equipment consisting of rock climbing gear. It's known to contain books that make the holder more intelligent, golems, dragons, secluded lakes, hidden passages (also lined with bookshelves), waterfallsnote that don't cause any water damage to the books behind them! the roots of The World Tree, and lots of booby traps.
The Exterior Library in Maoyuu Maou Yuusha contains all known knowledge from The Multiverse and is populated by a mysterious demon clan. The titular Demon Queen hails from that clan and used the knowledge she learnt from within to not only claim her current position, but also kick start the equivalent of the Real Life British Agricultural Revolution in the human world.
The library of the Crystal Ballroom in Nexus contains all the historical memory of (at least the known) universe.
Elder of the Universe and Silver Surfer foe, the Possessor, founded the largest university and library in the Marvel Universe on the planet Rus, complete with a master computer containing his vast knowledge.
Fables contains a massive library so large that the foyer is large enough to be a seat of government and contain objects of mythical size (Excalibur has literally become as big as the legend of Arthur). Oddly even though it belongs to all sorts of magical creatures it's never implied to be magical in any way except for its extreme size.
The Library of Dream (pictured above) in The Sandman is full of those books that were conceived by their authors but never written or completed. This not only includes things like G. K. Chesterton's The Man Who Was October, or P. G. Wodehouse's Psmith and Jeeves, but an awful lot of books like That Romantic Comedy Sci-Fi Thriller I Used to Think About on the Bus to Work. Word of God has it that it has an annex that contains everything that actually was written, too. We just never see it because it's so tiny compared to the rest of the place.
Superman: The Fortress of Solitude has information from the 28 known galaxies. Supes decides to store up Earth's knowledge as well.
There are a few super-libraries in the Star Wars mythos: The Jedi library seen in the prequels; an enormous data collection belonging to a former smuggler; a whole planet is devoted to being a galactic library. All three of these are implied to be the sum of all knowledge in the galaxy (or damn near, at least)
To the point where when, in Attack of the Clones, gravitational calculations prove that a planet MUST exist at a certain location, yet there is no record of such a planet, the librarian believes the library's records over the laws of physics. Just to drive home the point of how complacent the Old Republic had become.
The book The City of Dreaming Books by German author Walter Moers takes place in the city of Bookholm. On the surface, you can buy nearly every book in existence. But in the catacombes below, if you are able to survive long enough, you can find everything ever written. Somewhere.
Jorge Luis Borges' short story "The Library of Babel" describes a library that contains every possible book in the universe. This library is a lot less useful than most examples of this trope, because it is incomprehensibly large. So yes, the true story of your own death is in there, but so is every conceivable false story of your own death, with nothing to distinguish them. Worse yet, the library is randomized, with no catalog or organization to help you find something specific. And more than 99.9999% of the books are simply gibberish.
The Kingdom of the Isles has the library-fortress of Sarth, maintained by an order of monks. The library spans entire levels burrowed into a small hill, while an old dwarven mine beneath the hill provides even more room for expansion.
The Beast's library in Robin McKinley's Beauty. Might not have all the books that will ever be written, but it certainly has books that haven't been written as of when the story occurs.
The Great Library of Pandathaway in the Guardians of the Flame series appears to qualify — though its librarians also charge ruinously high fees to actually find the information within its cavernous shelves and chambers.
The Clayr's Great Library in Garth Nix's Old Kingdom series, which first shows up in Lirael, is under a mountain and doesn't limit itself to just books: odds and ends like sealed Free Magic beings and chambers large enough that it takes ten minutes to walk through them that contain only a pond, a tree, loads and loads of flowers and a fake sky (this is underground, remember?) are hidden here and there. Working in the library is apparently dangerous enough that whole parties of armed librarians are required for trips into the lower levels, and all librarians are required to have various weapons as well as a whistle and a clockwork mouse that will raise an alarm in case of emergencies on their person.
In The Neverending Story, Bastian creates a library with every story he has ever composed, for the benefit of a city of storytellers.
The Discworld explains the phenomenon of L-Space, which can turn any collection of books into a Library of Babel, thusly: Knowledge = Power = Energy = Mass, which distorts time and space. "A good bookshop is just a genteel black hole that knows how to read." That said, it also has more specific examples.
The library of Unseen University is a major "node" in L-Space owing to the sheer weight of accumulated knowledge distorting the space-time continuum. The library itself is pretty much a universe of its own where the library dome is always directly overhead no matter where you are, creatures such as the thesaurus lurk between the shelves, and lost research students have formed tribes in the stacks.
The Library of Ephebe in Small Gods is clearly modeled on the real-life Library of Alexandria, i.e., a serious attempt to collect all known books in existence - with the added feature of an earthed copper roof in case one of the Disc's myriad deities takes issue with something in its collection. It seems large but otherwise normal until it is burning down and The Librarian pops in and out via L-Space to save some of the books.
Death's Library is a variation - every person's life story writes itself into a book somewhere on his shelves. As you go back, the histories are written on scrolls, then animal skins, then stone slabs... One character asks Death's daughter (adopted) what came before the slabs, because some people would "quite like to know". She replies that she didn't get that far, as she was running out of candles.
Death also has a more straight version of this; in The Last Continent he is looking for information on the Discworld's version of Australia, XXXX. He walks into the library and asks for information on the dangerous animals, and is buried in books. He then changes the request to the non-dangerous ones, and one sheet of paper floats down, reading "some of the sheep."
The Galactic Library on Trantor, from Isaac Asimov's Foundation series, should count. At least until it's sacked. Add in the 'finished' copy of the Encyclopedia Galactica which is used to 'provide' the chapter quotes, as the Encyclopedia project is intended as a compendium of human knowledge so it won't be forgotten, too.
The Pnakotus Archive of the Great Race of Yith hidden deep underground somewhere in the Australian Outback, which is supposed to contain the history and combined knowledge of every civilization that has ruled, or will ever rule, planet Earth.
In HP Lovecraft's writing, some real world libraries also hold tomes of Eldritch lore. The Necronomicon, one of the best known examples, can be found in the British Museum, the National Library of France, the Widener Library of Harvard University, and the University of Buenos Aires. Some of these (particularly the National Library of France) are so old and so large that they probably count as real life examples without the terrifying books which drive people mad. note Then again, the National Library of France is where the original papers related to the Priory of Sion hoax were found, so it does contain written materials that have been shown to trigger delusions.
A Series of Unfortunate Events features several non-supernatural libraries which come close to this, including a massive system of filing cabinets, a collection of banned books, and a pile of valuable secret documents under a table.Every single book features a library of some sort which is plot important.
A Shout-Out to this. The library of the abbey in The Name of the Rose; though it does not literally contain every possible book, it is described as containing within it all the knowledge of medieval Europe, and entrance to it is forbidden. Also, the blind monk Jorge de Burgos is an obvious Shout-Out to Borges.
The Archives of the University in The Name of the Wind and sequels. It has no natural light, and it's so vast it's difficult to find anything, since no librarian could live long enough to implement an organization system, so there are different systems in place in different areas. It has The Big Board that marks locations in the world where teams of librarians are retrieving more books. There is one character, Puppet, who has lived in the Archives for years. There are "bad neighborhoods" of shelves with no organization whatsoever. There are secret passages that access the Archives from the undercity that was buried hundreds or thousands of years ago.
The Great Library in the Thursday Next books, which contains every book that will ever be written, and a few more besides.
Occurs regularly as a location throughout George MacDonald's fiction, notably Phantastes,Lilith, and Alec Forbes. Even in his realistic novels, the books in the library are definitely magical.
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Warehouse 13: Myka discovers that the eponymous Warehouse also holds a massive library containing first editions of everything ever printed.
Memory Alpha is the Library of Congress for the Federation. Since the Federation consists of multiple worlds, and new information is being brought in by Starships all the time, it's probably huge. Logically, there are Memories Beta through Omega to back it up in case the facility is lost.
In one of Diane Duane's Star Trek novels, the Enterprise returns to Earth for a resupply, and while everyone else is on shore leave, Spock stays behind to update the ship's computers with information from all of Earth's major libraries. (He finds it relaxing.)
In Doctor Who, there are two episodes dedicated to a library the size of a planet, which has long since been abandoned due to an infestation of Vashta Nerada.
Warhammer 40,000 has plenty of planetary libraries and eldritch stores of information:
The Black Library contains the collected knowledge of the entire Eldar race, but is hidden in the Webway and guarded by the greatest of the Harlequins' Solitaires. Only one human has visited it, but has sworn never to speak of what he found there, while the Arch-sorcerer Ahriman is obsessed with plundering its secrets for himself.
The Imperium has thousands, ranging from Alexandria-sized to covering all the planets in a system. Unfortunately they seem to think cataloging things is a sin, and only tend to pop up in the background when they're being razed by Orks or captured by Chaos.
Of particular note is the Adeptus Administratum offices on Holy Terra, where armies of robed scribes carefully record useless census data thousands of years out of date from worlds that don't exist anymore, then file the reports away in the kilometre-high stacks where they will never be read again. Meanwhile the Adeptus Mechanicus never deletes anything and stores the majority of the Imperium's scientific talent.
The Hidden Library of Tzeentch is even larger than the Black Library and contains every single scrap of knowledge, every thought of every creature across space and time, and is where Tzeentch himself concocts his eternal plots.
The Solemnance Archive, being a Necron record, has been expanding for the last hundred million years as its undead robot master, Trazyn the Infinite, adds new objects to his 'collection'. Such curios include the preserved head of an Imperial hero and entire armies of soldiers held in temporal stasis to form dioramas of historical conflicts.
The Library of Yves in the Tabletop RPGIn Nomine. Slightly subverted in that Yves' Library is actually well-organized ... it's the sheer scale of its contents that can make a search take days without assistance. Also notable is that the Library includes not just every book that ever existed, but every book that its author never actually got around to writing. (Such as the scripts for all seven seasons of Firefly.)
The plane of Mirrodin from Magic: The Gathering gives us the Knowledge Pool at Lumengrid, home of an entire race of Gadgeteer GeniusBadass Bookworms known as the Vedalken. While the Pool is technically less of a traditional library as it is a swirling mass of liquid wisdom compiled by its keepers over countless millenia, the Vedalken have made it their prerogative from Day 1 to collect as much knowledge as is concieviably possible.
The Duke's Archives, the personal collection of Duke Seath the Scaleless in Dark Souls. It takes of multiple rather large rooms and an entire tower(that also doubles as a dungeon), and considering that Seath is the creator of sorcery, they're no doubt on rather dangerous subjects. As Big Hat Logan found out.
The Dark People from The Longest Journey seek to obtain every book ever written, which they store in their library, located on a moving island whose location is a secret for but a few.
Touhou features Voile, the Magical Library note It's yet to be officially referred to as such, but that's the name of the music track that plays there in the Scarlet Devil Mansion's basement. It's large enough to allow for a roughly five-minute-long aerial battle over the bookshelves traveling in one direction without ever reaching the end. The library is maintained by Patchouli Knowledge, who spends her days locked up inside adding to the already-massive cache of knowledge - she's not just the librarian, but also the author of an unspecified proportion of the tomes in her library, and probably the overwhelming majority of the magic books in the library, given the esoteric rules for wizardry in the Touhou 'verse. While 100 straight years of this this have given her anemia, asthma, and Vitamin A deficiency, you are more than likely to find anything you could ever want in there (Marisa sure does).
World of Warcraft: The Library section of the Karazhan instance has bookshelves as tall as staircases, as well as books strewn all along the floor which can be picked up and used to give you one of a few buffs, depending on the tome. In addition to that, there are at least two libraries which might fit this trope even though they are physically small because they are larger on the inside than the outside, and/or because they have no normal doors and can only be reached by teleportation.
In Nine Hours, Nine Persons, Nine Doors, one of the doors leads to a massive library filled with books on several different subjects. It was used by the ship's former owner as a storage for his book collection.
The final Episode of Umineko no Naku Koro ni features the City of Books. The entire library is owned by Featherine and contains all the various books and stories (in the meta-world, various Fragments) that she ever created. The final battle between Lambda, Battler and Ange against Bern takes place here.
The Bibliothiki in Wapsi Square is an extra-dimensional library that contains every book ever written (but only things that have been written, no audio recordings). It is guarded by a sphinx librarian. It is implied that the Library of Alexandria was a physical manifestation.
Double Subverted in Gunnerkrigg Court. When the protagonist heads to the Court's library to get information for her school essay, you'd expect it to be an imposing, spooky, silent, mazelike place — after all, the Court shown so far is a massive imposing castle with supernatural inhabitants and qualities. Turns out, the library — at least, the sections not devoted to science and technology — is a single flimsy bookshelf with useless books. So the girls head to the old part of the library... which is an imposing, spooky, silent, mazelike place.
The Superhero School Whateley Academy library in the Whateley Universe isn't infinite, but it is enormous for a high school library, and contains lots of stuff human libraries shouldn't even know about, sealed off in private areas: alien books, Cosmic Horror Story books, ...
The Wiki World (a reference to The Other Wiki) of AH.com: The Series, which is an Alternate Universe Earth that has been wholly converted into a huge spherical space station dedicated to the preservation of all knowledge. So large that entire lost civilisations of "Edit Gangs" roam its abyssal reaches. Its rulers, the Wikimasters, govern it from an intimidating "Dark Cathedral". Subverted, however, when it turns out that in fact they're all just a bunch of pathetic anime nerds.
The online story Dominion And Duchy has one in the Galactic Library. It is run by an A.I. known as the Librarian and apparently holds the contents of the Great Library of Alexandria. The Librarian was apparently organizing it for the humans when they make first contact.
"The Library" in the desert in Avatar: The Last Airbender whose supernatural librarian, Wan Shi Tong, keeps humans outside because they have an annoying tendency to abuse his knowledge. The protagonists, after promising Wan Shi Tong that they were not going in the library with malicious intent, go up to the observatory and find the next eclipse — but only because they're planning to launch an attack. Long story short, Wan Shi Tong overhears them and gets very, very mad.
"If you're going to lie to an all-knowing Knowledge-Spirit, you should at least put some effort into it."
In "The Why of Fry" the Brain Spawn are constructing a database of all the knowledge in the universe, and once it's full, they plan to destroy the universe to make sure no new knowledge appears. In Fry's own words, "Now it's personal."
The Brain Spawn, amusingly, are actually scanning in EVERY SINGLE FACT (such as "2+2=4", "Puppies are cute", etc) not just tomes of knowledge or principles of mathematics. (Fridge Logic: If they wanted to store all mathematical facts, they'd need to record infinite facts of the form "n+n=2n" alone.)
Spoofed in "Mars University". All the literature in the world is in the Mars U library — on two disks. (Fiction and Nonfiction)
The Library of Alexandria gets this treatment in fiction. It held so much ancient knowledge that some say that if it had not burned down and been lost forever, technology would be significantly more advanced today. At the least, we'd know the content of many more classical works.
While nowhere near as well known as the library of Alexandria, the House of Wisdom, located in ancient Baghdad, was for its time the largest repository of knowledge in the world and actually held a great number of Greek and Roman translated pieces that may have originated from Alexandria. Unfortunately, it too was destroyed, in their case when the Mongols sacked the city.
Theoretically, the universe contains a record of every phenomenon that has ever phenomened; signals sent out contain information that can't be destroyed any more than energy can. The signal may become lost in noise, distorted and diluted past any hope of interpretation, and as useless as a full scale map, but it's there. Everything is a Great Big Library of Everything.
The British library could represent the closest modern version, at 170 million items. (Slightly larger than the U.S. Library of Congress) Its a legal deposit library, so by law, every book, pamphlet, magazine and newspaper published in the UK must send a free copy to be archived.