In the Bible, it says after the reign of each king "For the rest of his deeds and achievements, you can read book X". Except these days, you cannot.
The Talmud began as oral commentary on the Hebrew Bible by learned rabbis. Eventually these commentaries were written down and collected into a single document.
Each volume of the Romanike series has an appendix that rivals that of "The Lord of the Rings" in scope. Including a day-by-day breakdown of the narrative and the corresponding phases of the moon!
The author of Greystone Valley has a regularly updated website that has a lot of supplementary material only touched upon in the book.
Amelia Atwater-Rhodes hosts her own website with a great deal of supplementary information about her vampires, shapeshifters, and their world. Even more information can be found on her forum.
It may surprise some to learn that some of the most famous parts of The Iliad—the invocation of the Achilles heel and the Trojan Horse, for instance—are not actually in the Iliad. Instead, they're in The Odyssey. Similarly, the cause of the war and the recruiting of many of the warriors are told in outside sources.
To be accurate, the Iliad and Odyssey are the only surviving parts of a cycle of epic poems about the Trojan War. We do have descriptions of what was in those lost parts though, and that includes most of the background mentioned.
And to be exact, neither the Achilles Heel nor Trojan Horse appear in The Odyssey. They appear in The Aeneid, written by Roman Vergilius (Virgil) some 700 years later.
There's a huge deal of background material about Middle-earth written by J. R. R. Tolkien, if only you have enough time. First published were the appendices to The Lord of the Rings. For about twenty-five years before the publication of The Silmarillion, it was the best source of information about Middle-earth's backstory and went a long way towards giving it a historical feel. Then there are Unfinished Tales of Númenor and Middle-earth and the 12-volume(!) History of Middle-earth. All those books have tons of information about the history, culture and languages of the peoples of Middle-earth, as well as differing or earlier drafts of the stories.
It is uncertain how much of this material was actually intended for publication. Christopher Tolkien, appointed by his father as is literary executor, is responsible for all the works mentioned above. Much of the material is, to quote the other wiki, "unfinished, abandoned, alternative and outright contradictory accounts, since they were always a work in progress." There have been many accusations that Christopher has been publishing his father's wastepaper basket.
But then, how many other authors had a publishable wastepaper basket in the first place?
The Septimus Heap books all have sections at the end providing details for even the most minor characters. The series itself has also a true manual - or, more accurately, a "city guide" - The Magykal Papers.
Greg Egan stuffs his stories with heady physics that is almost impossible to fully convey without diagrams and calculus. He has interactive animated simulations on his website for the confused yet still interested. He's recently taken this Up to Eleven, posting eighty thousand words along with hundreds of illustrative diagrams to describe the alternate-universe physics he invented for Orthogonal.
Hal Clement, Robert Forward, and Tony Rothman are similar. Mission of Gravity (Clement) and The World Is Round (Rothman) have appendices explaining (some of) the physics involved in the novels, and pretty much any novel by Forward can be expected to have an extensive one.
George RR Martin's A Song of Ice and Fire series has ancillary material forming part of the role-playing games that is considered semi-canon (canon unless GRRM decides to change it) and throws some light on elements such as the history of the Targaryens and the Doom of Valyria. More important are the two 'Dunk & Egg' short stories set about 90 years before the books which cast significant light on background elements in the novels. A surprisingly large number of fans of the series remain unaware these stories even exist. The forthcoming World of Ice and Fire Book is also promised to feature extensive new canon information on the world and setting (Update: It does.).
Robert Jordan's The Wheel of Time series has extensive auxiliary material available for it, . Both The World of Robert Jordan's Wheel of Time and Wizards of the Coast's short-lived Wheel of Time Roleplaying Game feature extensive background information and maps that are considered canon.
Not to mention the huge glossaries at the end of each book.
The original Dune came with appendices that helped expand the universe, such as definitions of key terms.
Canon arguments are raging over the Dune universe, with the recent revelation that Frank Herbert's notes used by other authors to complete the Dune novels and write prequels were nowhere near as extensive as first claimed. As a result, some fans now refuse to consider any of the prequel or sequel novels by Kevin J. Anderson and Brian Herbert as canon, due to the extensive level of personal invention they brought to the setting.
The Dune Encyclopedia was meant literally to be the manual, or at-least official and authorized companion book. Though that was prior to the prequels by Brian Herbert and Kevin J. Anderson. Who have attempted to retroactively remove it from canon, despite originally having Frank Herbert's endorsement.
Some of the canon background notes and secret information regarding Larry Niven's Known Space universe has only ever been published in the long-out-of-print and now nearly-unacquirable Ringworld roleplaying game.
The Aubrey-Maturin canon has A Sea of Words, a 500+ page lexicon and handbook for readers who can't parse the series' prolific nautical jargon, drop-in historical references, and other arcane miscellany.
Night World clears up some ends left loose on the author's website, along with occasional sneak peeks. Link.
Les Misérables contains vast amounts of information on most of its named characters, regardless of their individual significance in the story. Although no adaptation of the novel thus far has made use of all the information, several of them, in order to remain canon, therefore end up retaining the names of the many minor characters and therefore confusing the intended audience. Possibly the instance where the background information in the novel has most effect is in the importance of the real historical figure Lamarque as a pivotal part of the plot. As this historical figure is only ever referenced rather than actually appearing, it is virtually impossible to understand this sequence in any adaptation without reading either a historical source or the original novel.
The Horatio Hornblower stories have a separate book that has diagrams of the sea battles and maps of the settings. It takes work to follow some of the technical parts of the battles without it.
An X-Wing Series novel, Starfighters of Adumar, has a set of articles called Adumar: Pilots Wanted made for the roleplaying game, which are partly in the form of the characters talking about those events for a documentary. It reveals something more about what happened after, while casually mentioning other things, like how Wes apparently died in Marvel Star Wars.
There's an old Star WarsDnD manual called "The Thrawn Trilogy Sourcebook" which largely is there to give stats for the characters and locations of the trilogy so that gamers can play them. (Thrawn's stats are slightly terrifying. Authority Equals Asskicking, indeed.) But it also comes with biographies that say a little more about the characters than could be gleaned from the books and tiny stories that illustrate some points. Some of these - for example, the bit about Wedge Antilles' parents dying on their fuel station when pirates took off without unhooking - were elaborated on later by other writers.
The entire Star Wars Expanded Universe is based on being a multimedia experience. Characters and events flip back and forth from movies to novels to cartoons to comics to video games to non-fiction sources all the time, making entire plotlines incomprehensible to readers/viewers without the complete picture who did not resort to online sources for clarifications. Those who read only novels would wonder where the heck did all those things the characters are alluding to happened, the gamers will not appreciate the appearance of random extras who are actually fan-favorites and important events and backstories being elaborated upon only in Visual Guides and RPG sources are commonplace.
The fourth and final book in The Dalemark Quartet is followed by a "Guide to Dalemark," a sort of glossary of terms, places, and characters. It contains a lot of supplementary information not mentioned within the stories themselves.
In case you were wondering just what the hell Gilead was, what purpose the Gunslingers had, and why the Tower's down to two Beams, try reading a book called Black House by Peter Straub and Stephen King. You'll actually get more information there about what The Dark Tower is all about that you will in all seven of King's books.
The Dresden Files has an RPG supplement that not only exists in-universe, but was edited for content by Dresden, and includes references to upcoming books.
Eoin Colfer released a tie-in book to the Artemis Fowl series which contained some "interviews" with the main characters and the author, the substitution cipher for the Gnommish alphabet, and two short stories involving Holly Short and Mulch Diggums.
Scott Westerfeld made a tie-in book for the Uglies series called Bogus to Bubbly which talked about all the world building and research that went into the series.
The Amber Roleplaying Game was coauthored by Roger Zelazny and goes into detail about metaphysics, power relations, and characters' hidden motivations. In this case, though, enough is burlesqued to make the game work as an RPG that it's difficult to tell what's canon. (Among other things, the RPG offers completely different character sheets for every character, the first reflecting the Unreliable Narrator's descriptions and the others offering contradictory "real" explanations.)
The Honorverse has the Pearls of Weber, containing almost 20 years of collected statements from the author, along with the Jayne's Intelligence Review series and the House of Steel compendium.
In addition to The Black Book of Buried Secrets, the official companion book/guide to the series, The 39 Clues has a plethora of trading cards and a website where you can input the cards' codes and unlock secret files with additional information on the series' universe.
In Greek Ninja, additional details about the characters that aren't mentioned in the story are given on a separate page.
The Warrior Cats franchise has a lot of information only available as Word of God or in the Field Guides. The pain is eased by the authors eventually working this information into the main books, such as Tallstar's Revenge revealing who the main character's father was in series when it had been Word of God for a while (but only after 4 whole years, and Scourge being his brother was still only implied), and that most of it isn't too important to the series. But still, you have to feel sympathy for the people who don't know who Nutmeg, a character who appears in the allegiances of Tallstar's Revenge and nowhere else in the series, was because they didn't download the Warriors iPod app (she's Firestar's mother), and the people who wonder who the hell Daisytail, a random StarClan cat that keeps appearing, is.
In addition to the main stories, the website for Relativity also has "Side Stories" which provide additional background details of the characters. For example, at the beginning of the series, ordinary everywoman Sara Wolff is dating a billionaire named Martin Bling. The story "Those Who Have the Gold" explains how she met him and how their relationship started.
The author of Twisted is also an artist and has drawn all kinds of supplemental material relating to her were-roller coaster's anatomy and function.
The Mistborn Adventure Game rulebook features a fair amount of previously unknown lore, especially since Brandon himself helped write it. The most prominent example is the Treatise Metallurgica, which fills in the previously unknown Feruchemical powers of aluminum, duralumin, chromnium, nicrosil, cadmium, and bendalloy.
Though it's not exactly necessary to read The Zombie Survival Guide to understand World War Z, the book does expound on the history of the solanum virus and the ways to combat it. The book itself is given several passing references and is implied to have been made during the initial stages of the outbreak. It's also spoken of by the interviewees as being imperfect, and so specific to survival in North America as to be nearly useless elsewhere. It recommends as essential things that were just flat-out unobtainable for people living elsewhere. Todd Wainio dismisses it as some survivalist trash (complete with jerkoff motions), and the head of Radio Free Earth points out that not many people outside of North America would have a gun, or even running water.
In Spectral Shadows there's quite a few instances of this. Any information on characters not yet appeared can only be found out if you read the Character List. Some additional information on characters and plots are also only found in said list or by reading the author's LiveJournal.
In Vampire Academy, Aaron is Lissa's and Mia's boyfriend and a royal Moroi. His particular clan is not mentioned in the series. "Vampire Academy: The Ultimate Guide" reveals him to a member of the Drozdov clan. Kind of makes sense since Mia's parents were established as servants to this clan.
Dora Wilk Series has Toadies, short stories anthology which was initially conceived to fill in the gaps left in the novels. Among others, it tells of how Leon came to regard Dora as his adopted daughter, how Szelma and Eryk became an Odd Couple and how the conflict that poisons Dora and Bruno's relationships started.
One Nation Under Jupiter: Much of the information about the setting is located in online side material outside the book itself.
The novelizations introduce several key characters such as Naar or Alyss. (Good luck knowing who or what Alyss is otherwise.)
Also the Magnamund Companion; nothing really vital, or that doesn't come up elsewhere, but loads and loads of awesome world-building. As well as a Lone Wolf board game and a short Choose Your Own Adventure with Banedon as protagonist, providing some backdrop to Book 1.