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 and 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.
The celibacy thing, as explained in Fanon Discontinuity, is ignored due to Lucas saying they could have sex, but couldn't form attachments. Think about that for a few seconds.
Moving away from sex, most fans believe that Luke was under the Dark Side's influence in the Dark Nest Trilogy.
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".
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.
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.
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.
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.
Michael Myers, the antagonist of Halloween never dies in either of the two original timelines, presumably surviving the end of both The Curse of Michael Myers and Resurrection, the last in each respective timeline. And with the start of a remake, it is clear neither timeline is going to be "ended" by the film makers. So, Chris .R. Notarile created a fan film (with professional voice actor Tom Kane in it) depicting the death of Michael Myers at age 60, from the rage inside him (as Dr. Loomis predicted in Halloween 5). It could fit into either timeline.
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.
In The Boondock Saints fanon, it's generally agreed that Connor is the older twin.
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...
Sharpay often has a cutesy nickname that her mother calls her by, to go with Ryan's "Ducky".
Sarah's mother in Labyrinth is usually referred to as either "Karen" or "Irene". No one seems to know for sure what her actual name is.
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.
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.