Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
The eternal temptation...
"These two methods clearly do not agree with one another, which means one of two things: either I'm terribly over-analyzing the content of the illustrations of a beloved children's book, or the bunny's bedroom is moving at extremely high velocity relative to the earth, so that relativistic time dilation makes the six-minute rise of the moon appear to take an hour and ten minutes. Calculating the necessary velocity is left as an exercise for the interested reader."note It's 0.9963 c, or roughly 668 million miles per hour.
The other reason you should use protection when reading Fanfic.
Fanfic comes in many varieties, but many stories fall into the major categories of "more of the Same" (also called "Original Flavour"), which attempts to tell a new story using the setup and style of its source material, and "Mythos Building", which tries to cement the writer's personal theories into the pseudocanon of the source (and usually getting a Sue laid in the process). The latter tend to be more memorable, but at a price.
Many of the fan theories which make their way into Fanfic seek to "fix" something the writer believes to be wrong with the source. The fans usually put a lot more thought into this than the show's writers ever did (though show writers have gotten a lot more attentive in recent years, primarily because of the growth of this kind of fan activity). They often come up with answers to questions that either make not a whit of difference in the end, or are more fun without an answer than with.
Naturally, these theories often venture way out into fantasyland. When the theory makes you say, "Oh come on!", the fanfic author has stepped over the line into Fan Wank.
When the show itself canonizes such a theory, it's a Retcon or a Re Vision or one of the two varieties of Continuity Porn. When a fan does, it's Fanwank. Note, however, that Retcon is a value-neutral word, while fanwank definitely carries a connotation of crap. On the other hand, theories that get popular can become fanon.
The etymology of 'wank' shows that it means 'indulgence', particularly any kind of major self-indulgence. Not surprisingly, this leads to it being British slang for masturbation, though it's mostly just their own egos that such writers are stroking. Mostly. The term was coined by Doctor Who fan and Doctor Who Expanded Universe writer Craig Hinton, who was no stranger to it himself, and applied it to his own work.
Particular common triggers for fanwank include:
Code Geass gets a lot of it even ignoring the shipping and endless debates about Character Alignment. A good portion comes from all the questions left unanswered by the staff either by choice or as a result of being Screwed by the Network. This includes things like C.C.'s real name, the true nature of Geass, the origin of Suzaku's superhuman abilities (and their suggested connection to Geass), the true fate of Kallen's supposedly dead brother Naoto and countless other potential topics.
The exact laws and origins of the Cursed Springs of Jusenkyo — how much water is needed, what the exact temperature is, how much of your body has to be splashed, what sort of liquids would qualify, why drinking doesn't trigger it, whether the original victim drowned to death or was merely submerged (thanks to an early translation error and the Guide's insistence that the stories are all "tragic"), whether the springs confer any aspect of the original creature's personality, and whether the curses are age-specific.
Another common fan wank on the Jusenkyo Curses is adding the secondary effect of actively attempting to induce the transformation rather than simply making it possible. Typically by making the victim a water magnet and invokingContrived Coincidence to wet the victim if they haven't changed for too long. This idea is often used either (or both) to avoid Rule of Funny explanation of where the convenient buckets/thrown water comes from in more deconstructive works, or to explain why Ranma gaining partial control over his curse doesn't simply turn into an effective cure due to the canonical Aversion of the Second Law of Gender Bending: even if the water trigger of his curse is removed, and replaced with a voluntary mental triggering or other far more controllable trigger, the curse still forces Ranma to spend some time in his cursed form.
A gag scene in the Herb saga led to one of Ranma 1/2s most enduring fan wanks. In the story, Herb mentions he hates female Ranma because she resembles a monkey he threw into the Spring of Drowned Girl - a monkey, who in turn caused him to be cursed. As a result, the idea spread that anyone who falls into the Spring of Drowned Girl ends up looking like the original girl who drowned there. The creation of the Spring of Drowned Akane, introduced into the manga long after this piece of fan wank was created, just made matters even worse.
Some fans wonder if maybe Happosai deliberately drank the Nanniichuan water that was supposed to be Ranma's cure in the final manga chapters, as it's a bit hard to mistake spring water for sake on first taste and Happosai is both extremely selfish and fixated on Ranma's sexy female body.
Ki Attacks get a lot of this. Everything which isn't explained in-universe tends to be attributed to Ki manipulation. Mousse having a Hyperspace Arsenal up his sleeves? He's using Ki to compress space. The Happo Fire Burst explosives? Conjured from Ki. Akane's "signature" Hyperspace Mallet (which she doesn't even use that often)? Obviously a Ki construct. Kuno's implausible use of his Bokken? Clearly, it's reinforced with his Ki!
This probably in part comes retroactively from Naruto, as such Hand-Waving is canon in Naruto; everything out of the ordinary is done with Chakra.
Sailor Moon fanwank has an Epileptic Trees theory which suggests that Sailor Pluto is deliberately engineering a timeline where 95% of the Earth's population is killed off in a thousand-year glaciation period in order to produce Crystal Tokyo. At no point does the anime ever say anything along the lines of 95% of the population dying in a disaster. The anime notes that Usagi awoke a frozen world from slumber in the 30th century and ascended, whereas in the manga, there was no disaster at all and the utopia evolved naturally. So the entire theory is Fan Wank piled upon Fan Wank.
Sailors Uranus and Neptune are lesbian lovers. Fans more familiar with the censored English dub are often uncomfortable with this and have produced multiple stories that usually involve Uranus becoming a man or being a man in a former life and getting this "corrected", usually by magic. This was not helped by the bizarre Save Our Sailors website promoting the idea of a male "Prince of Uranus" being accidentally reincarnated as a female Sailor Uranus as canon. In their eyes, that removed the homosexuality of the pair.
The so-called Turn A Bang theory from the Gundamverse. After a scene in ∀ Gundam depicting a period of history that was made up of clips from various other Gundam shows—shows that were originally toted as alternate universes—fans began trying to construct a timeline that would justify having all the shows in a single universe.
Naruto fanfiction is very nearly the most written anime fanfiction on ffnet, mostly due to what Kishimoto decided to wait to reveal: the name of the Fourth... Fans thought his name was "Arashi ___" with the common idea being "Arashi Uzumaki" because everyone thought he was Naruto's father. In truth, his name is Minato Namikaze, his actual situation (reincarnated as Naruto after sealing the Kyuubi in himself?), village laws (the idea of "Clan Restoration Act" for a dying clan), the concept of a council (sometimes split into a Shinobi Council and a Civilian Council), shipping of characters, Naruto's mother, bloodlines, members of Akatsuki, and even now, there is plenty to speculate about, like whether or not Madara is actually immortal.
In the Sgt. Frog Western fandom, there is a lot of Fan Wank debates of whether or not the alien frogs, known as kerons, can have hair or not, some fans going as far as to saying their all wigs and or cannot have hair because they are 'frogs' and label any keron with hair, as a Mary sue. This originally started on DeviantArt and then Tumblr, on a fandom confession blog which has since been deleted.
Which is taken to extreme amounts of stupid given the sheer number of characters with facial hair, and head hair that have appeared in both show and manga, but these fans will not accept it unless they are seen brushing, washing, or any other kind of hair care treatment.
Which gets even more stupid, when in one episode, Keroro ends up with a mutant mole hair on his forehead that grows to a extreme length.
Stephanie Brown and Cassandra Cain of the Batman family being either in Hong Kong or at various beach resorts and probably on a variety of recreational drugs, following the New52 reboot. Neither have been acknowledged on panel as existing.
Stephanie Brown is coming back in the weekly comic, Batman Eternal. Cassandra is still MIA, but due to some changes made to the canon, would have to have some radical changes made to her backstorynote Lady Shiva, her mother, was de-aged into being around the same age as Nightwing, so Cass would either have to be a child, or have a completely different mother.
V from V for Vendetta's gender. It's pure fan wank in both the graphic novel and film that V, a person consistently referred to in both the novel and movie as "he" and "the man from room five" is Valerie, a female character we only see in flashback, presumably after some serious surgery.
When a mini-series pitted roughly-analogous Marvel and DC characters against each other with the winners determined by fan vote, Wolverine unsurprisingly got more votes than Lobo. Since even comic book artists don't have enough imagination to figure out how Wolverine could actually beat someone who's fought Superman to a standstill (and this was back when Wolverine just healed pretty fast, and wasn't functionally immortal ... but Lobo was) the fight took place entirely offscreen, which lead to a common fan explanation that Wolverine bribed Lobo to take a dive.
Later made canon in an issue of Lobo. Except it was implied that Professor X paid Lobo to take the dive as to spare Wolverine's ego and reputation.
The ending of Inception was intended to be an open ending, with the viewer left to decide if it was a dream or real. This has not stopped fans from finding "evidence" that suggests the director intended it to be one or the other.
Due to its rather simplistic storyline, Enchanted fans have been left with the task of interpreting several plot threads left at the end, including the rhyme and reason behind Edward and Nancy's last-minute hookup and how someone as naive as Giselle would react when she learns about sex.
In-universe fans of Galaxy Quest have constructed a whole map of the ship and worked out explanations for everything on it - which pays off when the actors need that kind of knowledge aboard the real ship.
Which is some subtle Fridge Brilliance as the Aliens who built the ship must have done the same thing from watching the same "Historical Documents"
The Star Wars franchise is rife with fan explanations and justifications. For example, the Kessel Run being made in a unit of distance:
The Kessel Run involves ferrying goods between two ships moving away from each other. The faster a ship, the less distance it has to travel to catch up.
The Kessel Run involves navigating through or around a dangerous asteroid field. Less maneuverable ships have to take a long, circuitous route around the most dangerous areas; better ships can take a shorter path right through the dangerous middle.
Han was testing Luke and Ben, to see if they would correct him, thus proving they knew a thing or two about space travel. Luke didn't catch the mistake, and Ben was fine with Han thinking they were both rubes. The last revision of the original script (previous versions didn't notice the problem) had Han making inaccurate boasts and "Ben reacts to Solo's stupid attempt to impress them with obvious misinformation."
The official story as set down in the Han Solo Trilogy is that the Kessel run is dangerously close to a black hole and the closer you're able to fly to the black hole the shorter the distance and the faster the run. This was a major Fan Wank before it was retconned into the actual story.
This was later retconned in the novelization of the film credited to George Lucas (although written by Alan Dean Foster), where Han states that the ship made the run in less than 12 "standard time units".
Luke uses the Force to choke a Gammorean in Return of the Jedi ... but isn't that using the Dark Side of the Force? Not if he only used the Jedi Mind Trick to make the Gammorean think he was choking! Or maybe it's only considered truly dark if you use the Force choke with intent to kill someone, as opposed to just staggering them.
All Force users have high Midichlorian counts!? They have to have meant to say that Midichlorians are attracted to high concentrations of the Force; they're a result of Force use, not the cause, right? RIGHT!?
Alternately, the ability to use the Force could be the result of a genetic kink, and Midichlorians are proteins produced as a by-product. This may be a case of Artistic License - Biology, but it's a better explanation than the one in the prequel trilogy, right? And as a bonus, it explains why Force-sensitivity can be inherited and why there aren't all that many Jedi even at the height of the Old Republic.
The Jedi thought "bringing balance to the Force" was a good thing, but it actually meant that Anakin would kill all but two Jedi, so there'd be the same number of Jedi as Sith. (Never mind that Word of God says "bringing balance to the Force" meant destroying the Sith, and Anakin just did it much later than the Jedi expected.)
There are also some interpretations suggesting that what originally unbalanced the force was Anakin's creation; Darth Plagueis manipulated the midichlorians to create life, which wasn't supposed to happen, and so the only way the force could be 'balanced' was Anakin's death, which would by its nature defeat the Sith.
Why didn't Chewie get a medal at the end of A New Hope? You see, Wookiees don't believe in medals and awards. The Rebels wanted to give him one, but he refused. So instead they made a contribution to his family back on Kashyyyk.
However, in the comic book version continuance, Han and Luke put Leia up on a table to give Chewie a medal since it would have looked "undignified" for her to attempt it during the previous ceremony.
Havelock Vetinari's sexuality - which way does he bend? (To extrapolate from the canon that the Patrician of Ankh-Morpork is naturally self-sufficient, austere and celibate is way too boring.)
If Vetinari is gay, which recurring male characters would he get off with?
In the unlikely but rescuable situation of Vetinari being straight, which female characters would he seek to have a scene with? - averted in later books which refer to a generally rumoured past relationship with Lady Margolotta, which survives in some form to the present continuity.
The girls in the Monstrous Regiment's Last Detail. Gay or what? (Well, almost certainly Tonker and Lofty...) And who in this troupe of military lesbians is doing what to whom and with what implements?
Susan Sto Helit and Jonathan Teatime. Given time, or an alternative universe, would they have got it on?
On a more intellectual level, the issue of the much-mangled and twisted Discworld timeline - which was eventually explained in universe as the History Monks having to repair the timeline, twice, after some idiot human broke it into little pieces.
And the meta-wank thrown in that the History Monks to exist because of continuity errors that Terry Pratchett makes when he writes the books.
The big issue in The Lord of the Rings fandom (and quite possibly the fanwank debate to rule them all) is the question of whether or not the Balrog had wings. Other, smaller debates include whether or not Tolkien's elves have Pointed Ears and what color Legolas' hair was in the book.
Or the true nature of Tom Bombadil - was he a random nature spirit, or the avatar of the world?
Why didn't the Eagles simply fly the ring to Mount Doom? Choose from corruption by the Ring, corresponding evil aerial units, Eagles are Chaotic Good and don't answer to orders, can't intervene, or it just would have forshortened the series.
Ever since the first Sherlock Holmes stories were published, many learned writers have tried to figure out why Dr Watson's old war wound was in the shoulder in A Study In Scarlet and in the leg in The Sign of Four. Answers range from "He was actually shot in the buttocks and was too embarrassed to say this" to "He was shot on two separate occasions." There's an organization called The Baker Street Irregulars (it's been around since the 1930's) who devote a great deal of time and effort to filling in all the gaps and resolving all the discrepancies they can, including "Exactly where was 221B Baker Street?" "Why was Dr Watson sometimes James and sometimes John?" and "Was Holmes' dressing-gown purple or mouse-coloured?" (Some of these essays have been published in the book 17 Steps To Baker Street.)
Interestingly enough, the James / John discord was made fun of in the film Young Sherlock Holmes and the Leg/Arm discord was made fun of in the BBC's modern reboot Sherlock, in the first episode "A Study in Pink" where Watson limps as though he were shot in the leg, but the limp is in fact a psychosomatic reaction to the real wound in his shoulder.
Much of Star Wars EU, especially post-EII ICS, is this; thought not only technical details are wanked up - Force powers are too.
Live Action TV
The backstory of the main character in Doctor Who, specifically:
Retconning away the revelation of the Doctor's half-human lineage from the 1996 Made-for-TV Movie.note River Song said it best: "Rule One: The Doctor lies."
Explaining how the Doctor has a granddaughter in light of the vehement insistence by many fans that no character on the show (and most especially not the Doctor) can ever, ever, be suggested to engage in a certain physical activity often responsible for producing parents of grandchildren.
The Klingon Forehead Problem in Star Trek - Klingons from the original series had smooth foreheads, while in every other work, they have ridges. Roddenberry initially said Klingons always had the ridges but TOS just lacked the makeup budget to show them, while it was later acknowledged in Deep Space Nine as their having had smooth foreheads when the crew meet 23rd-century Klingons. In Star Trek: Enterprise, this retcon was given a canon explanation as Genetic Engineering Gone Horribly Wrong resulting in a virus that infected a significant proportion of the population.note Going into non-canon works, this was shown in Star Trek Online to have been cured some time in the late 23rd century by an unaffected Half-Human Hybrid from the 24th/25th century in a Stable Time Loop. Before this became the canon explanation, there were various fan theories such as cosmetic surgery to pass as other species for covert operations, to being a single group not representative of their species as a whole.
Adding to the confusion is when Klingons from TOS appeared on DS9 and suddenly had ridged foreheads. One theory regarding this is that those Klingons got cosmetic surgery to make themselves look like "normal" Klingons.
iCarly: Copious amounts related to shipping. One large pro-Seddie group interpret any form of communication or interaction as supporting their ship.
The "Seddie is going to happen because Dan said so" shippers. See Shrug of God for why they can never actually back their claim up with any evidence.
In Stargate fandom, one of the most obvious and yet never directly addressed questions is why all the aliens speak English. Various theories have emerged, the most popular being that the stargates themselves act as translators.
Though at some point the producers do mention that they elected to ignore the language barrier for the sake of efficiency and a less contrived feel.
Some have speculated that the travel through the Stargate somehow implants individuals with foreign languages and the reason why this didn't originally manifest is because the Earth Stargate uses a haphazard jerry-rigged control system. McKay complains that the Earth gate ignores hundreds of important commands that normal gates use.
The penchant Skins has for ambiguous series endings leads to lots of this.
How I Met Your Mother is specifically designed to spawn this, with fans spending pages of threads on Television Without Pity and other sites guessing who the mother is, how the many events Future!Ted says are important to the story with factor into the story of the mother, what is the significance and context of many orphaned, Noodle Incident-like flashforwards that Future!Ted promises to explain later and how they will fit into the future storyarcs. There has also been constant wank trying to justify how one of Ted's previous girlfriends might be the mother, as well as speculation about how Ted will meet the Mother (it was finally revealed that he met her at Barney's wedding), and theories about what the goat in Ted's bathroom on his birthday was about (it was part of a multi-sided Kudzu Plot and wound up putting Ted in the hospital) and the most recent topic of wank is who Barney's bride is from the flashforward to his wedding (the main argument is between Robin or a new love interest), and what the reason for the Mother's presence there is.
On Merlin, Morgana and Morgause are established as half-sisters, though it's never definitively said whether they share a mother or a father. There's evidence for either Vivienne or Gorlois as the shared parent, but in series 3 it's revealed that Morgana's father is not Gorlois at all, but Uther (making her half-sister to Arthur). Since Morgana and Morgause continue to refer to each other as "sister" after this, most fans assume that Vivienne is the shared parent. Added confusion comes out of the fact that Gaius initially called them "half-sisters" (long before he knew that Uther was Morgana's true father), a statement that doesn't make sense unless you assume that Morgause had a father who wasn't Gorlois (otherwise they would have been assumed to be full sisters).
The Dungeonomicon is a pretty massive Fan Wank trying to justify (among many other things) the economics, social structures and fantastic locales of D&D.
A common form of Fan Wank in Dungeons & Dragons 4th Edition is "refluffling," or using the mechanics of a power as written but changing the explanation of how the power works to better fit a character concept. It's commonly done with characters using the Martial (non-magical, weapons and skill-based) power source, to explain how someone with no magical powers can turn invisible (you see, he's really just hiding so well he'd might as well be invisible), control an enemy's actions (you're not making them jump off a cliff, you're staggering them, and it's just dumb luck that they happen to stagger 20 feet straight toward a cliff edge), etc.
Recently officially sanctioned on the D&D website; there was an Insider article both describing the practice an encouraging it.
Earlier than this, it was specifically mentioned as something that should be done with Warlock powers so that they fit your character's contract, and used to explain why the contract labels for powers were dropped after the Player's Handbook — the labels led people to an attitude that they could only pick appropriately-labeled powers for their warlock, when they had only been intended as a guide and if you really wanted a power that wasn't appropriately labeled, you could just change the fluff to match.
Farcast for Eclipse Phase is an entire year of fanwank, where the author set out to see if he could produce a year's worth of material for the setting just to see if he can.
In the backstory of Warhammer 40,000, there were 20 Space Marine Legions before the Horus Heresy, where 10 of said Legions rebelled. In order prevent another organized revolt in the future, the remaining Legions were split into much smaller Chapters. Two of the original twenty Legions—and whether these Legions stayed loyal or rebelled—were intentionally left blank, so Space Marine (both loyalist and Chaos) players could fill in the details themselves when making their own Chapter/Legion, if none of the established lore fit the tone they were going for. The explanation for the identities and fates of these two blank Legions has caused no end of Fan Wank.
Later novels set during the Horus Heresy expanded considerably on the time of the Space Marine Legions, including many previously unknown (and not a few retconned!) aspects of, for example, the Alpha Legion. But all in all, they do touch about the "Lost Legions", and while they are never named nor their Primarchs brought up, dialogue suggests they did, in fact, go with Horus—and were wiped out for it. A rather chilling line refers specifically to either Primarch Russ, the Space Wolves or both being their "executioner" because (according to a guy in the story who would know these things) Russ was chosen by the Emperor to deal with such matters within the Legions and the Wolves were the Emperor's personal death squad. It should be noted much earlier short stories and novels inferred similarly that the Lost Legions:
A—Were lost to Chaos.
B—Were promptly exterminated.
C—And it was Russ that pulled the trigger.
Why, exactly, we have never seen a male Mithra in Final Fantasy XI. The official explanation for a lack of male Mithra PCs was originally simply that they're unadventurous and so never leave home, to the consternation of those who are uncomfortable with the concept of the Non-Action Guy or just of not being able to play a cute catboy. With the release of the first expansion, we see our first truly wholly Mithra town and still no men (due to early fears of running into the PS2's technical limitations), the explanation was elaborated as the slightly less plausible "they never leave the Mithra homeland" without clarifying that Kazham wasn't it, and thus the Fan Wank engine got the push start it needed. The most popular fan explanation is that they're too rare for use as anything but dedicated breeding stock, and what man would complain about that job, up to and including being chained up in the shadows? Wings of the Goddess does finally show one male Mithra in a cutscene (clothed, no less), but this may be too little, too late. Similar questions exist for the "all-female" Viera race found in Final Fantasy Tactics Advance, Final Fantasy XII and other Ivalice - bound games.
The Legend of Zelda series is inspiring quite a bit of timeline fanwankery. Also, the Shipping Industry is quite profitable in that area. There's a huge debate about Link/Zelda or Link/Midna.
The many, many, many efforts to make a coherent timeline out of the series. Furthering this endless Fan Wank is the infuriating fact that Aonuma and Miyamoto have confirmed the existence of a timeline, and made the placement of a few games Word of God, but refuse to reveal the document itself to anyone not working with the games.
...until the release of the 2011 artbook/encyclopedia Hyrule Historia, which contained the entire timeline.
The theory that Ocarina of Time split the timeline in two started out as fanwank, until it was confirmed by Word of God. Happened the same with the fact that Link and Zelda are different people in most of the games. The Wind Waker settled it... just to open up a new fanwanky question: Which exactly is the relationship between them? Descendants? Reincarnations? Both? Different people altogether?
Again, Hyrule Historia reveals that Ocarina actually split the timeline in three, and that a few of the Links and all of the Zeldas are related, though it doesn't even touch on the whole reincarnation issue (although it was strongly hinted in Skyward Sword, specially in Zelda's case).
Which opened up more wank, since one of the timeline splits hinged on Link dying before Ganondorf could be defeated.
Kingdom Hearts has enough fan wank going about Nobodies and all associated mind screws that they've caused multiple spoogenamis.
The Another Side, Another Story special ending from the first game deserves a special mention. The quantity of Fan Wank that single video originated rivaled all the LOST and Zelda timeline theories.
The thing about Kingdom Hearts is that there is an abundance of rules and guidelines within out-of-the-way sources or bits of dialogue in-game. After the first six games, there was enough canonical information to demystify many of the more confusing parts of the series. It's just that there are a lot of seemingly arbitrary rules that can be hard to keep track of, even if they do make things make sense. Hence, fan-wank.
In the Pokémon Gold and Silver games, whether Raikou, Entei, and Suicune are cats, dogs, or whatever. Many forums moderators decided that people are free to call them whatever, but if there's any argument they are "officially" the three legendary gerbils.
The arguments are stupid anyway because they're all based on various mythological creatures. Entei is based on one of the Lions of Foo, Suicune on the Qilin and Raikou on Raiju. Really just calling them 'beasts' would've saved a lot of time.
This is what happens when you base an extremely popular FPS on an Excuse Plot. Fans of Team Fortress 2 have been going mad over various details about the world of the game: the characters' background, the in-universe mechanics (respawn or replace?), etc. However, Valve is slowly giving the players breadcrumbs through comics and videos.
The Silent Hill series by its nature encourages this in their Fandom; Game FAQS is filled with exhaustive plot and character analyses. A sure way to troll any fan forum is to cut down Epileptic Trees with the insistence that it's all just deliberately Invoked Mind Screw on Konami's part.
The popular Assassin's Creed: Brotherhood fan theory of Cesare Borgia being the creator or inspiration for Abstergo Industries... because he said the word "cleanse" once.
Some fans of the Ninja Gaiden series try to fit in the events of the original arcade game (which is largely unconnected to the NES version and its later sequels, save for a few superficial similarities) into the continuity of the later console games by claiming that the two player characters (a pair of ninjas, one in blue and another one in red) are actually Ryu Hayabusa and his father Joe (or Ken, depending on the version) undergoing a mission that they went through before the events of the Xbox and NES games (despite the fact that the player characters in the arcade version were never given identities).
There was a Transformers fan-author named Stormcloud, who seemed bound and determined to use every Beast Wars character not in the show in his 'fics. The end result was fight scenes that were so step-by-step and plotted out that they resembled a pre-publishing RA Salvatore, with character names made up of bad animal puns.
Go to the YouTube clip about the creation of the Transformers taken directly from the G1 cartoon it came from. Behold the number of comic fans trying to explain to innocent viewers how it fits into the Transformer God Primus origin from the comics, despite the fact the G1 Transformers cartoon made no reference to Primus, and as far as the TV producers were concerned, this was the intended origin for the show.
A rather interesting example occurred with Batman Beyond. Fans theorized that Terry and Matt's lack of resemblence to their father, specifically their black hair, genetically improbable given their parents' hair colors (red and brown respectively for Mary and Warren), had a role in the divorce. Flash forward to the Justice League UnlimitedFully Absorbed Finale "Epilogue," and guess what? Bruce Wayne is revealed to have been the boys' biological father, with Warren's genetic material having been, unbeknownst to anyone but CADMUS, overwritten with his. According to the series' writers, this decision was influenced by the realization of said improbability.
Aside from the two Care Bears movie continuities, as the Headscratchers mentioned, what happened to Dark Heart after he turned human, and for that matter, why did he attack them, why did he care about a girl that saved his life once? What was his backstory, and speaking of which, the backstory of all of the villains and the pre-Wishing Star bears and cousins?
Let's just say that the fans put a lot of thought into analyzing the physics, economics, politics, and magic of the setting. In particular, discussions of exactly how powerful Celestia and Luna are, both in the physical and political sense, crop up a lot. Entire fanfics have been written primarily for the authors to explain and justify why their particular set of Fanon makes the most sense.
In "Daring Don't", Twilight and Rainbow Dash briefly engage in this In-Universe concerning the Daring Do series.