The incidents between the Martian Successor Nadesico TV series and movie were explained in various Japanese-only video games, novels, and radio shows, leaving American fans puzzled at the movie's very different tone.
The anime Doomed Megalopolis features a confusing narrative quite difficult to follow for those who have not acquainted themselves with the cultural references or the source material Teito Monogatari. This is partly because the anime adapts only the first 1/3rd of the novel and tries to force in a conclusion to make up for it's lack of completeness.
A large amount of key information useful in understanding the story can only be found in the supplemental materials for Neon Genesis Evangelion.
There was actually another manual that was released later, then basically overtook the previous manual in canonicity. No one had translated that into English yet. This is technically the third time it happened, since the Spin-Off Game decanonized the first manual called the Red Cross Book. It's likely they'll continue making new manuals with mildly and noticeable different interpretations of what's going on until they finally go bankrupt.
Curiously, though the new Chronicles share many major points of info with the PS2 Game, they curiously completely ignore all references to a certain group of Secret Benefactors that don't ever show up within the Anime at all. In combination with Gainax's OFFICIAL stance on the Game being that "All plot details were made specifically" for the Game, it's possible we got Retconning Manuals on our hands here.
The Renewal of Evangelion DVD contains the director's cut editions of episodes 21-24. New footage was added in order to make the plot more comprehensible and answer a few lingering questions (such as Kaworu's origin and (some of) the circumstances behind the war with the Angels).
The Koko Wa Greenwood OVA literally directs the viewer to a specific chapter of the manga to explain a reference.
This is because the second OVA happens after the next 4 (it even refers obliquely to the plot of 5 and 6). AND it's a sequel to a story they didn't animate.
Bleach provides a series of databooks that contribute to a broader understanding of how the main manga should be interpreted. The databooks offer further information on published events and characters while also adding teasers and hints for events and characterisations that might be expanded upon in the future.
For an example of a series where all the materials are becoming officially translated for the West, see .hack//SIGN and its sequels — to get the full story, you need to read a novel, watch a 26 episode anime series, play four games, watch the four OVA anime episodes bundle one with each game, read four more novels, and read a three volume manga (and/or watch the 12 episode anime adapted from it, but that isn't canon so it won't really help you), preferably in that order. That's not counting the non-canon spinoffs or the sequel project, which consists of much the same combination again.
The 3 .Hack//GU games, in fact, took place after the 26 episode series .Hack//Roots, directly continuing the story of the protagonist Haseo. However, the first GU game was released several months before the first DVD of Roots was translated and released. Therefore, gamers who had not been watching fansubs of Roots were completely in the dark about who Shino was, what had happened to her, and why Haseo was going so mental over her; especially since the game was purposefully vague on details.
There's going to be a third project that takes place in the real world too.
On the other hand, watching the anime first will completely spoil most of the plot, especially one particularly dramatic twist that occurs at the end of the second game. So it's not really clear what order these were meant to be seen in.
Not everything has made it to the west. .hack//Zero still hasn't been translated. Seeing as it was set in The World R:1 and they've moved on past R:2 to R:X, it's doubtful it will see light of day. Or be finished in Japan for that matter.
Pokémon: The First Movie could not be fully understood without the CD drama Birth of Mewtwo to accompany it. It doesn't help that the partial animated adaptation of that CD Drama, which was basically new scenes added to the beginning of later Japanese releases of the first movie and treated as additional parts of the film, was cut out from the dub (an English adaptation was available, but only on the bilingual Japanese DVD releases). Fortunately, 4Kids later included this for American fans in the Pokémon: Mewtwo Returns DVD.
Pokémon 2000 has two instances of this: First, the scene near the end where the collector found the Ancient Mew card on the shore in the wreck of his ship. This scene makes sense in English because they added a line earlier where he said that it was the object that started his collection. In Japanese however, you had to be lucky enough to get the program book given out at theaters. Also, that program book gives his name, which is never said in dialogue (it's Jirarudan, and his ship is called Hikoukyuu). To complicate things, in English he has two names—the captions call him Gelarden (an acceptable if not slightly convoluted Romanization of the original) while the English movie book calls him Lawrence III. As in Japanese, no name is said aloud.
There are two novels by Takeshi Shudo, a major writer for the anime, that give insight intothe world. It tells us stuff like what happened to Ash's father, Brock's siblings are only his half-siblings, and that ten-year-olds are legal adults (they can get arrested, they have to pay taxes, they can get married...). A lot of the info isn't canon nowadays but it does make sense in the Kanto days, like how Officer Jenny was able to jail a bunch of kids so easily.
In Yu-Gi-Oh!, there are various questions in the anime that are All there In The Manga, mostly characters' backstories.
Still questionable though, since the anime already contradicts aspects of the manga as it is.
The Macrossuniverse includes significant amounts of supplementary canon from books, comics, and video games in addition to the series and OVAs that were actually filmed.
The final fate of Hikaru, Misa and Minmay is buried in the manual for Macross M3 — They were lost with the rest of the crew and passengers of SDF-2 Megaroad after they apparently encountered a black hole.
Masaki Kajishima, main writer for the Tenchi Muyo! OVA-verse, has regularly released supplemental material, such as novels and self-published doujinshi, with information about that continuity. One of the reasons for releasing the spinoff series Tenchi Muyo! GXP before the Tenchi OVA Revival series was to introduce some of the new characters and other elements from the novels to the audience that hadn't read (or wasn't able to read) them.
Similarly, Ken's backstory in Digimon Adventure 02 has him disappearing into the Digital World as a kid and reappearing a short time after; later, we see a scene of him adventuring with another kid and getting infected by a Dark Seed. These are both references to the game where he teamed up with Ryo.
Unfortunately, none of these games were released outside of Asia, so this resulted in some confusion.
The supplementary manga and Sound Stages of Magical Girl Lyrical Nanoha explains how Nanoha learned the Bind spell during her battle with Fate, who that Linith woman was in the Lotus-Eater Machine, what the heck happened to Arf in the third season and what that gift from Reinforce that Vita was talking about was.
The supplementary files also contain a fair amount of information on the plot. Not only does the StrikerS Sound Stage X explain how many of the spells work, but it also provides information such as how the N2R squadgot its name, and specific information on the long-standing consequences of Teana's partner being outed as the real killer in the Mariage case.
Want to know the backstory for One Piece Strong World's villain, Gold Lion Shiki? You have to either go read the supplemental "Chapter 0" or watch the OVA based on said chapter.
Likewise for One Piece Film: Z, where the titular villain's backstory is revealed in Volume 1000, a complementary book that was given as a present to Japanese movie-goers. However, this is actually subverted, as part of Z's backstory is mentioned in the movie itself, and the book only reveals it in full.
The OVAs of Gravitation take place after nearly the entire manga, only obliquely hinting at its events in flashbacks; Yuki's troubled past isn't even mentioned.
Xxx Ho Lic and Tsubasa Reservoir Chronicle have ended up so interconnected that it is nigh impossible to understand one without reading the other. And even then you wish you had the option to phone Ohkawa and demand an explanation.
The Saint Beast anime series and OVAs are more illustration than substantial, the whole story happens in the audio dramas.
The Kiddy Grade artbook contains a timeline for the main characters and the changes in attire as well.
Code Geass actually has quite a few forms of All There in the Manual, including Sound Episodes (released on separate CDs) as well as Picture Dramas and short story inserts with the DVDs. Unusually, Bandai localised all these into English, with the Sound Episodes being part of the Limited Special Collector's Ultimate Edition package.
For Mobile Suit Gundam SEED there is, in addition to 10 Drama CDs (six of which are set before the series starts, three set during the series, and one post-series), 10 novels that go into more detail about the characters and events, several manga series (Mobile Suit Gundam SEED Astray), and a few OVAs and TV specials, an official website that has a lot of extra information about the Cosmic Era... including a highly detailed timeline that goes back about 100 years before the start of the series.
Not to mention at least one plot point from SEED (Kira surviving the Aegis' self-destruction) was explained in the Astray manga.
The original Mobile Suit Gundam Universal Century series is the king of the trope. Novels, sourcebooks, even supplementary material printed in model kit instruction manuals.
Mobile Suit Gundam Wing has a backstory that was supposed to be placed into episode 27 and 28 - but was shafted due to internal politics. Thus, the explains-a-lot backstory was put into a sidestory manga that, while released in the USA, wasn't released with a high profile... and isn't in print anymore. There's also another pair of sidestories that explains some events between the two Wing works, with the same release problem in America. The fact that there was a third one released that barely amounted to a fan work published by a company trying to cash-in on the phenomenon in America didn't help things at all.
Mobile Suit Gundam 00 took the concept of All There in the Manual and ran with it from the very beginning of its airing. Gundam 00 Sidestories include 00P, a photo novel type series that covered events before the series proper and dealt heavily with the development of the Gundams, 00V, a series of documents on variations of existing MS from the series with accounts of said machines told from a historical perspective, and 00F, an Astray style manga that took place at the same time as the series and did its best to fill in certain gaps. But it doesn't end there, there's also 00V Senki, the follow up to 00V that elaborates on some of the machines from 00V and features stories from all over the timeline, including AFTER the conclusion of the series, 00N, a new series of documents, and 00I, the follow up to 00F that gives way more insight into the Innovades from the show and covers events that took place between the two seasons. On top of that you have your usual novels, sourcebooks, audio dramas, and model kit manuals, and Gundam 00 is certainly making an effort to take the crown of All There in the Manual king. Only 00F has been released in the US.
Mobile Suit Gundam F91 may be the biggest example of this in the MSG franchise. As a result of originally being a TV series that was cut down and compressed to a movie partway through production, most of the story is completely dropped from the movie. The movie does not show how Seabrook and his friends defeat Cosmo Babylonia and the Crossbone Vanguard. So, to actually finish the movie's story as well as find out various things that happened within the movie but were skipped because of time constraints, you have to read the manga or novels. Which have never been officially released in the US.
Gundam in general does this in the form of various magazines and Gunpla infosheets. Yes, you read it right, many of the debates among fans will often end up with one side pulling out the supplemental info shipped with various Gunplas. And just like any of the highly-controversal Gundam SEED(Destiny) canon info, these are known for being extremely prone to "retconning over and over", with MG and PG Gunpla infosheets often outright contradicting their earlier HG counterparts, and MGs of different mechas don't tend to treat other very well either...
See also Zoids, whose main continuity (Battle Story) is almost entirely told in the model kits. None of this information ever gets translated.
JoJo's Bizarre Adventure has several enemy character and later Stand names just outright omitted in early story arcs. Most of the villains in Stardust Crusaders go entirely unnamed in the original publications, only to be given names later on in the volumized editions and art books. This was particularly egregious when Viz translated it into English the first time around and gave the name "Rubber Soul" to the character Steely Dan, when Rubber Soul is the name of a character that appears earlier but goes unnamed. The anime series fixes this by at least giving characters' names in eyecatches. Later parts of the manga also give character names and Stand names either explicitly in the text, as part of a cover page, or again later in the volume versions.
The OVA series also suffered from this, as it featured only the Stardust Crusaders plotline but began the OVA halfway through it and then from there was a pretty abridged version of the original storyline. This was rectified years later when a second OVA from the same studio released a prequel OVA series to cover the first half of Stardust Crusaders, which was still extremely abridged, but at least explained what the hell led up to the first series' events. The English adaptation released all of the episodes in chronological order, and added a narrated summary of the events in Phantom Blood and Battle Tendency, the first two arcs of JoJo.
The Five Star Stories by Mamoru Nagano contains some of the most ambitious worldbuilding in anime and manga history, a lot of which gets little exposure in the series proper. Fortunately, the English editions come with sections from the sourcebooks printed in the back of each issue, including full-colour illustrations.
Devil May CryThe Animated Series doesn't bother to fully explain Dante's connection to Trish or Lady, their respective histories being found in the first and third game. Amongst others.
The series are meant to be viewed in the order of Games 3, 1, the anime, 4, and 2. So missing the games does indeed leave you with a lot of unanswered questions when it comes to the anime series.
The hosts for Papillon's homunculi in Busou Renkin were all humans that pissed him off for one reason or another, as detailed in their character bios in the tankobons. Good luck understanding Papillon's hallucination without reading the bios first.
The artbooks provide a lot background info as well.
Any character in Axis Powers Hetalia that might come across as a Flat Character probably has most of his/her personality only displayed in the profiles. Some characters can only be seen in the author's blog.
There's also a lot of references to past events that you might not understand without either pausing to read the history annotations or looking it up. Then again, pretty much everything in that show is related to past events, even Chibitalia's dress.
Himaruya had a habit of this with his earlier series as well. Many characters in Susume Kitakou Housoubu and Barjona Bombers were never really fleshed out or even got to appear in the series, although illustrations and (lost) profiles served to provide information on them.
Baccano!: Generally, the anime is relatively self-contained and understandable without turning to the Light Novels (sans one scene in episode one that is Left Hanging), but there's obviously a lot of background that doesn't find it's way in, and there's also quite a bit that goes on after the events in the anime. Good luck finding translations, though.
The canon of Weiß Kreuz is distributed across two anime series and an OAV, a good many drama CDs, and several manga and short stories. Fortunately the first anime series is pretty well self-contained, but in the absence of the material from the OAV and drama CDs the drastic changes between it and sequel series Weiss Kreuz Gluhen make no sense at all. Naturally, only the two anime series have been officially released to western audiences.
In the American release of the Read or Die OVA, the post-it notes in Yomiko's apartment are mistranslated because the translators apparently didn't realize "Nenene" was a name; she doesn't show up in the OVA but in the manga and subsequent TV series, Sumiregawa Nenene is Yomiko's best friend.
In Death Note, you never do find out L's real name. Unless, of course, you get the book with all the supplemental information in it or watch the last live action film. It's L Lawliet.
The Sakura WarsOAVs and movie are based on (and mostly continuations of) the games. Somehow America got the former without the latter.
Random splash pages in Fairy Tail will be entirely dedicated to a member of the titular guild. When it's a main character like Erza, or a minor one with a decent amount of attention like Elfman, it will tell you random things like how Erza terrorizes fashion designers into making her armor, of that Elfman once lost a bird and never realized the one he found was not the same. If it's a background character who gets roughly one line per arc at best, it will give detail into their past and personality. Much of this information ends up getting incorporated into the anime as filler.
Overall, the original Light Novel series of Slayers goes into detail of how the magic system and the like works better than the anime does, but not in clarity, as both forms of media tend to contradict themselves. The only true "manual" for the series is a long series of interviews by creator Hajime Kanzaka, and he flops around and whimsily comes up with answers to questions to the point that he's making every potential canon fact up on the fly. The only truly solid facts are extended backstories of the main characters (especially important in regards to Idiot Hero Gourry because he is the only major character whose background gets no spotlight in any media). Even then, some incidents, such as Gourry and Sylphiel's first meeting and Lina's great fear of her older sister are never explained.
Also, there are two radio dramas that act as extensions of the Slayers PremiumNon-Serial Movie; a prologue and an epilogue that both set the stage and tie up loose ends (including how Naga sided with the Big Bad of the movie and how Amelia was saved after being blown off to an abandoned island); naturally, they're only available in Japan. The manga adaptation as a whole does a better job at telling the story.
Some information in Naruto can only be found in databooks. Most of the Tailed Beasts and the names of the other Jinchuuriki and Kages were shown in the supplementary materials long before they were revealed in the actual manga.
The Last: Naruto the Movie, unlike the other films, holds relevance to the overall plot as it's events take place between the last two chapters of the manga, even being regarded as Chapter 699.5
At the end of every Future Diary volume, there is an Omake that may explain certain things that were not very obvious, such as how and why the 3rd, 4th and 9th were targeting each other, and how they began to focus on Yukki. It also gives a little background info on some of the other future diary holders.
There is also Mosiac and Paradox, which focus on the Ninth and Akise, giving more info on the Sixth as well.
A few of Chibisan Date's characters only appear in the author's blog.
Puella Magi Madoka Magica's website gives extra information on the witches and their minions and familiars. To some extent, anything in runes counts, as few viewers take the time to decode it.
The DVD releases come with audio dramas. The first one is about the cat that appears only in the Title Sequence. The third one expands on Kyoko's past, and how she knew Mami. The second one is probablynot canon.
Puella Magi Madoka Magica Portable has even more witches, particularly the witch forms of Mami, Kyoko and Homura. Eventually, the latter witch appeared in Rebellion, the movie sequel to the anime, bringing it out of this territory, but the other two still have yet to make an appearance in the main series.
In Mai-HiME, the sound dramas, specials (often characters narrating about themselves) and art books often provide more information about the characters, and the short story "Natsuki no Prelude" contains details about how Natsuki became a HiME and her friendship with Shizuru.
Similarly, the Mai-Otome sound dramas provide bits of backstory from the main series, such as how Tomoe met Shizuru, some of Yukariko's backstory (she was a Meister who had to cancel contracts due to her masters falling in love with her) and Mai and Natsuki's early days at the academy, including how Natsuki became Shizuru's room attendant.
Much of the back stories and family life for Ronin Warriors in Yoroiden Samurai Troopers can only be found in supplemental books and Drama CDs.
A lot of additional information for the Tiger & Bunny series shows up in the audio dramas (which are included with the Blu-Ray releases) or in supplemental guides. Information within them ranges from amusing tidbits (such as all the heroes' first crushes) to more plot-relevant elaborations (like who Kotetsu's wife was and how he met her).
In Future GPX Cyber Formula, there are several drama CDs and supplemental artbooks that details the backstories about the characters, such as in the last drama CD, which revealed Kaga's backstory, how Kaga got his scar on his forehead and why he warned Hayato about the Zero Realm in ZERO (he was in a racing accident with his best friend Eiji which was caused by the Zero Realm and Eiji was killed).
The iDOLM@STER - Some events in the anime series make a lot more sense if you've played through the game it's based on and unlocked the backstories for the idols.
Supplemental materials for Ghost in the Shell: Stand Alone Complex have very detailed information about the world of the show, including the political backdrop of the story (which is only hinted at in-series) as well as plenty of weapon descriptions.
In Girls und Panzer, a fair amount of information can be found in the spinoff materials
The OVA series sheds light on how the school ships work.
The manga shows the battle against Anzio, which took place offscreen in the anime, in its entirety.
The Little Army manga has two fairly significant revelations - that Miho actually enjoyed tankery while she was young (struggling to find people with whom she could do it, and a reason to do it) and that Maholoves Miho and wants her to find her own way of tankery.
A lot of details of the setting, such as actual rules of Tankery (like how only prototypes and production models made prior to the end of World War II are allowed) and world history, are only found in supplementary materials, and never mentioned in-show. The Blue-Ray supplements also mention the existence of "Unlimited" Tankery. Primarily practiced in America, in contrast to "traditional" Tankery followed in such places as Japan, Britain and France, "Unlimited" Tankery dispenses with the many mechanical limitations imposed in the traditional rules, and allows absurd levels of customization, such as removing tank armor and installing 12-cylinder engines, to the point that the tanks in questions look like anything but tanks. This particular discipline was also a source of controversy within the global Tankery Federation.
Attack on Titan: At the end of certain chapters, an extra page goes into detail on certain aspects of the world. Examples include a roughly to scale picture of the Walls and how much area they protect and details of humanity's technology. The anime incorporates this information by displaying it during its Eye Catches.
Senki Zesshou Symphogear often has large amounts of information about the mechanics of the Symphogears and Noise hidden away in keywords (such as the Symphogear system having over 3,000,000 limiters as well as how the sync ratio-enhancing drug LiNKER works), and it also detailed Hibiki'sDark and Troubled Past and Disappeared Dad before those issues came to the forefront in the third season, GX.
In Cute High Earth Defense Club LOVE!, this is downplayed with Tazawa's first name (Masuya), as Tazawa only comes into the story at episode 5 of 12, season 1. The online manga plays this straight regarding some of the villainous trio backstory (e.g. how Kinshiro and Arima met) but the final chapter, found in the print version only, has to be understood by watching the canon material.