Magical Library

A magical library is a mystical library that is explicitly magical or is infused with magic. These libraries tend to be small and hidden in a remote area. They usually contain dangerous and forbidden spells, arcane Spell Books and priceless Ancient Artifacts and MacGuffins. They also may have supernatural books such as Tomes of Prophecy and Fate and Tome of Eldritch Lore. The libraries also might be home to monsters, creatures and Magic Librarians that are there to protect the library. The library might be quite old, and may even be as old as the universe itself.

Due these things being valuable and it would be disasterous if these items fall in the wrong hands. These libraries are usually hard and almost impossible to find without a special map and well guarded. The objects that allow the library's location to be found are sometimes scattered across the world. The heroes and villains alike might have to engage in a Gotta Catch Them All plot in order to have access to the library's valuable information.

If the magical library is easily accessible for most people it's usually part of a school. The protagonist's may regularly visit the school library to find out how to solve a problem or gain information about the current plot. Characters that are a bit more rebellious might simply steal from the library instead, setting up the main conflict.

These type of libraries tend to appear mostly in Fantasy, Urban Fantasy and works that have a Fantasy Kitchen Sink.

Examples:

Anime and Manga

The Great Library in Yami to Boushi To Hon no Tabibito consists of books that contain every single world of the multiverse down to the smallest detail. And it also comes with Magic Librarians.

Comic Books

Lucien's library in The Dreaming. Has many books which were never written.

Film

The Librarian films are about a librarian of this type of library. Not only does it contain legendary and magical books, but also all the world's greatest and most dangerous treasures.
In the movie What Dreams May Come a briefly seen library . It is massive and there is no floor, only water. People just fly to get the books, also, it is a heaven.

Literature

The library of Unseen University in Discworld leads to other dimensions thanks to the sheer weight of accumulated knowledge distorting the space-time continuum. This is known as L-Space. The library itself is pretty much a universe of its own with all the magical books, library creatures such as the thesaurus or the kickstool-crab, and lost tribes of research students inside.
- There's also Death's library of biographies, one for everyone in the world, where those for the living are still in the process of writing themselves.
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.
Harry Potter: The school library is this, especially the restricted section. In the first book, when Harry was trying to find out who Nicholas Flamel was, he sneaks in, opens a book, and it starts screaming at him, attracting Filch.
In The Last Apprentice series, it's implied that all good spooks have a library with information on denizens of the dark and how to defeat them. We only specifically hear of John Gregory's and Bill Arkwright's, though.
The Library of the Clayr from the Old Kingdom. It's carved out of glacier and is the largest repository of magic books and monsters around. It's keept in order by Crazy Prepared Magic Libarians.
The Magic Treehouse, whose books can transport the reader to the event described.

Live Action TV

The Sunnydale High Library from Buffy the Vampire Slayer as it's directly over the Hellmouth. And has a ton of weird magic books that Snyder totally doesn't get being there, naturally.
In Angel the evil law firm Wolfram & Hart has a library of books but you don't have to search for the right book. They have some enchanted books which you tell what book you want from the library and the text appears in the book.

Tabletop Games

The Mage: The Ascension from White Wolf had a stat for arcane library.
Mage: The Awakening also has a stat for an arcane library. In both cases the stat is called Library.
In the Ravenloft setting, the lich-king Azalin has a library which houses the self-updating life stories of every sentient being who has ever been born in his domain of Darkon, or who's entered it and stayed long enough to lose all memory of their previous life. Destroying your own book is one of the few ways to recover from Darkon's insidious Identity Amnesia effect.

Video Games

In Touhou, there's Voile, the Magical Library. Maintained by Patchouli Knowledge, who spends her days locked up inside adding to the already-massive cache of knowledge and Spell Books. 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).
According to Elder Scrolls lore, the Daedra Prince of prophecy and fate, Hermaeus Mora, lives on a plane of Oblivion called Apocrypha, an infinite library full of Tomes of Eldritch Lore.
Final Fantasy V gives us the Library of the Ancients, where there are possessed books, a book split in two by the splitting of the worlds, and a book that burns other books...

Web Original

The website The Wanderer's Library (an offshoot of the SCP Foundation verse) is set around an apparent extradimensional library which houses numerous books of secret lore.