Various explanations for the inconsistencies of how time travel works between the three Terminatormovies are fanon. The Terminator movies (and the TV show, for example) never state how it works, just that it does.
Wookieepedia, the Star Wars Wiki, has a fairly complete list of fanon elements that found their way into the official continuity, either as an intentional homage or due to the authors mistaking them for canon.
A particularly irritating bit of fanon (covered in the blurb of thisDarths & Droids strip) that many people still can't seem to understand is false is the idea that the "Balance of the Force" refers to the Balance Between Good and Evil and was reached when Anakin killed all but two of the Jedi (Obi-wan and Yoda) leaving the number of Jedi and Sith equal. This is especially weird/frustrating when you consider how many people use the Jedi not thinking this would cause most of them to die out as "evidence" for them being stupid/corrupt and/or the prequel trilogy being an Idiot Plot. Word of God has stated that "Balance of the Force" means some Jedi, no Sith, and that the previous Jedi order didn't need to die. (And this line of thinking doesn't make much sense, either: an equal number of Jedi and Sith [unless that number was zero] wouldn't engender balance in anything and just cause an unending and highly escalated war.) As once was said, a lot of fans miss the idea that the Dark Side isn't Yin. It is Sin.
There's also the idea that the midichlorians somehow create the Force. There's no indication of that in Canon, and according to Wookieepedia they are merely indicators of Force Sensitivity. There's even an in-universe theory establishing that the Force creates the midichlorians.
Regarding homosexuality in the GFFA, Bioware caught hell for Juhani, whose article is still a mess from people arguing whether or not she was written as a lesbian. Stanley Woo, her writer at Bioware said unequivocally that the answer is YES.
And then we get Karen "Canderous Ordo in Drag" Traviss who settled at least part of the issue by stating that the Mandalorians don't give a shit.
Male Exile. How many times was Wookieepedia edited for that one?
Ditto with so much as acknowledging Revan could be played as a female. Even the mention of it caused flame wars for a while. Give me a nickel every time some fanboy screams "Revan can't be a girl, it's CANON" and force me to pay a dime back every time someone says "Exile's a chick. It's CANON," and I'd still have enough money for a five-star supper and gas money.
We don't know what kriff means, just that it is used emphatically. It is assumed it means "to have sexual intercourse with".
It is almost certain that the upcoming sequel trilogy will completely override all Expanded Universe material following Return of the Jedi, although whether fans will care is a different story. However, it will be a dark day for Wookieepedia, which will need to mark a vast portion of its articles as being non-canon.
Many fans believe that Anakin didn't believe Palpatine's conspiracy theory about the Jedi trying take over the Rebublic; he only went along with it because Palpatine had something he needed. James Luceno even made this canon in the Expanded Universe. However there is nothing in the movie itself to indicate that Anakin ever believed otherwise.
Because the movies never actually bother to explain how Shmi Skywalker became pregnant with Anakin while apparently a virgin (other than through a vague line about him possibly being "conceived by the Living Force") many fans have adopted the explanation that he was somehow conceived through Darth Plagueis' experiments with midi-chlorians. Since Palpatine explicitly says that Plagueis could "create life", it's plausible that he could have created a child with abnormally powerful Force abilities.
The Big Lebowski: a popular theory among fans is that Donnie is in fact Walter's imaginary friend.
Which doesn't make sense, because the Dude also acknowledges him a few times during the movie. Unless he is both Walter and the Dude's imaginary friend. But if he was, why would they go to a funeral home after he dies? Unless that was a dream sequence... And so was The cremation scene. The Stranger also refers to Donny, meaning he's also an imaginary friend. And who is bowling with them the whole time?
The Jesus also acknowledges Donny during the movie too.
As does Gary, the bartender at the bowling alley.
Essentially every character who appears in a scene with Donny acknowledges his presence in some way.
The Usual Suspects: There are a number of fan theories that identify Keyser Soze as any member of the cast you care to name. In the director's commentary, the filmmakers express puzzlement over this phenomenon, saying they felt the end is pretty clear.
In The Film of the Book of Prince Caspian, a geeky boy attempts to flirt with Susan at the train station in the first few minutes of the film. A small group of fans have grown attached to him, and christened him Warren.
Figwit the sexy elf from The Fellowship of the Ring was noticed by fangirls and anyone else who got bored during the Council of Elrond scene; he was adopted by the fandom and given his name, and when he reappeared in RotK, there was much squealing and choking on popcorn. Incidentally, he's played by Bret McKenzie of Flight of the Conchords.
Figwit seems almost to have been embraced by the creators; Bret McKenzie's character returns in The Hobbit trilogy, as Elrond's personal herald, no less, with the name "Lindir" (which means "singer.")
Ditto for The Chronicles of Riddick. It IS extremely easy and quite possible to argue that it takes place sometime in the Dark Age of Technology. In fact, the events of the film line up quite perfectly with much or all that is known about the Warp. While the film makers may or may not have intended it, it is in fact perfectly reasonable to say that Event Horizon is the first ever WH40K movie.
A surprisingly large number of people sincerely believe that the name of Edward Norton's character is Jack. In fact - and this is lampshaded in the film - his true name is never revealed, although an argument can be made that it is, in fact, Tyler Durden. Notably, the novel is a bit more unambiguous about the last point, as it includes a brief scene after The Reveal where the Narrator shows his driver's license to Marla to prove that "Tyler Durden" isn't his real name.
In the script and behind the scenes they did use the name Jack, though as an allusion to the Reader's Digest articles written by an organ in first person discussed in the film.
Another popular theory is that Calvin and Hobbes is the prequel to Fight Club, with the Narrator being an older Calvin, Marla as Susie, Bob being an older Moe trying to be The Atoner and Tyler as a vengeful reincarnation of Hobbes.
The fandom for Inception has unanimously decided that Eames' totem is a poker chip. This is fleetingly implied in the film but never explicitly stated.
Another of his fan films depicts Freddy Krueger Being captured by Pinhead sometime after his death in Freddy vs. Jason, and torn apart by Jason Voorhees, (the mind of) Michael Myers, and (the presumably-deceased soul of) Leatherface, with Pinhead stating "Your reign of evil is now over.", indicating that he will never return again. This contradicts Freddy vs. Jason vs. Ash and its sequel, but these are an alternate sequel to Freddy vs. Jason than Jason X, which couldn't take place after Freddy vs. Jason vs. Ash 2: Nightmare Warriors because history is altered to prevent Freddy's transformation into a dream demon, thereby preventing him from resurrecting Jason at the end of Jason Goes to Hell: The Final Friday.
If Chad is not dating Taylor, he's dating Ryan 99% of the time. Probably has something to do with the sexy baseball scene in the second movie...
Even fans who don't ship Ryan/Chad assume something went down in the locker room after that baseball game, not helped by the fact that they're wearing each other's clothes in the next scene.
Sharpay often has a cutesy nickname that her mother calls her by, to go with Ryan's "Ducky".
Sarah's stepmother in Labyrinth is usually referred to as either "Karen" or "Irene". No one seems to know for sure what her actual name is.
The official movie novelization establishes her as Irene, though Karen remains more popular among fans.
Labyrinth has a very active fandom, especially fanfiction and fanart, and most of it draws upon the same fanon:
Sarah's last name is Williams (it's mentioned in the film novelization, but not in the movie itself)
Jareth is Fae. He's only ever referred to as the Goblin King in the movie, but his behavior and Blue and Orange Morality lead a lot of fans to believe that he's part of a larger society of faeries.
The Goblin Kingdom, and the Labyrinth, are located in a magical world called the Underground (drawing from David Bowie's song of the same name, featured in the opening and closing credits of the film). Whether or not it's actually below our Earth is debatable.
Sarah goes to college to study English or theatre.
Jareth and Sarah reunite when she's in her twenties, and they have a torrid romance and get married.
Jareth and Sarah have some kind of psychic or magical connection, so that they can sense when the other is in danger.
Toby has no memory of the events of the film. (Realistic, since he was a baby, but not necessarily true.)
Jareth's mother is Jadis, the White Witch. (Popularized by Pika-la-Cynique's multifandom comic Girls Next Door)
It's a popular theory among Quentin Tarantino fans that at least some of the events of Pulp Fiction occur on the same day as the bank heist in Reservoir Dogs; in particular, the fact that no cops are around to stop Jules and Vincent while they're driving a car covered in blood in the middle of a busy street during broad daylight is because they're occupied with the heist and its disastrous aftermath.
Alternately, many fans have proposed the theory that Pulp Fiction is a direct sequel to Reservoir Dogs, and that the mysterious briefcase in Pulp Fiction contains the diamonds from the heist in Reservoir Dogs. This has some basis in fact, as Word of God has confirmed that the briefcase was supposed to contain diamonds in the original draft of the script.
Many viewers of Avatar believe Eywa is manipulating both sides of the conflict to achieve her ends of getting rid of the RDA. This is based on absolutely no canonical evidence whatsoever. She doesn't even visibly interfere until Jake takes some time to explain the situation to her, and the Na'vi are about to lose their decisive battle, when she could've just Zerg Rush'd the RDA at about any time.
Even though it takes place in an alternate timeline, it is generally accepted among fans of the 2009 film Star Trek that Kirk was sent to Tarsus IV after the "car incident", and was present for the massacre on the colony just as the Kirk of the "main" Star Trek timeline was. It's not unusual for this to be a profound influence on his character in fic. The notion has also crept in that nu!Kirk studied under Hoshi Sato, who was said to be on Tarsus IV at the time of the massacre.
Also, the vast majority of reboot fanfic writers write Kirk's stepfather as an alcoholic, ultra-abusive, evil child molester and his mother as depressed and emotionally distant.
And after the scene in the 2009 film with Kirk have strange reactions to everything that Bones injected him with, it has been decided by the fans that Kirk is essentially allergic to a large percentage of medications.
Connected to the above, popular theories arise concerning Hawkeye's backstory, many inspired by the mainstream comics. The most common are Clint was a Circus Brat and/or has a criminal record (which again, is basically his comics backstory), formerly served in the US Army or in some kind of Law Enforcement division, is a single father with a young child, is dating/married or was formerly dating/married to Bobbi Morse, that Bobbi Morse is the mother of the aforementioned child, and many more.
Planet of the Apes: It's accepted by many that Zira and Cornelius coming to the past and Caesar's birth there altered the 'verse's history, greatly speeding up the ape revolution and making it happen much earlier than the one that led to the events of the first film.
And on a connected note, the aftermath of "Battle" is often seen as being different than the original timeline, meaning the world might or might not have been destroyed as it was in 'Beneath' but no one knows for sure.
If the closed loop theory is held, there's wide speculation that anger at Caesar led to him being erased from ape history later on, leading to the scrolls Zira and Cornelius read having Aldo as the first to say "no".
In Bill & Ted fanfics, if either of boys' biological mothers' whereabouts are mentioned, typically Bill's left him and his father, and Ted's mom is dead (Going with one of the other few B&T fanfic trends of making him a Woobie)