The Russian Tolkien fandom has a set of very specific Fanon, mostly First Age-related, most of which was established by published big fanfics. (Yes, there is a bootleg Expanded Universe version of Arda in Russia, illegal in most of the world but legal in Motherland itself.)
The (common to most Tolkien fandoms) notion of Celegorm the blond
The notion that the Feanorians and their warriors wore a uniform of red, black and silver
Fans have certain ideas about mortal women in Middle-earth. A woman always wears a dress, never breeches. If a woman is on a horse, she always rides sidesaddle, never astride. Some fans enforce this even when the woman must hike or ride for long distances.
Fans often add the title "Lord" or "Lady" to characters. Fan fiction has "Lord Erestor" and "Lord Haldir". In canon, a lord or lady is almost always the first man or woman of some place or people, like Elrond "Lord of Rivendell" (LotR Book II, Chapter 1), Denethor "Lord of Gondor" (V, 1), and Éowyn "lady of Rohan" (III, 6). An exception is Gandalf as "Lord Mithrandir" (V, 1). Some fan characters have "Lord" or "Lady" as a rank without anywhere to lord over. Lord Kinsey in Home with the Fairies lives in Minas Tirith, and might be lord of nothing but his own household. In some fan stories, "lady" is no longer a title, but a polite label for any random woman, like lady Helanthir in Troubled Waters.
Dwarves: The word "dwarfling" only appears in fan fiction. Tolkien never used "dwarfling", but in LoTR Appendix A, a young-adult Dwarf is a "stripling", and an Orc addresses an adult Dwarf as a "beardling".
The word "elfling" only appears in fan fiction. Tolkien never used "elfling". The suffix -ling is for "little", so an elfling is a little elf, an elf-child. Tolkien does use similar words: little Ents are "Entings" (LotR Book III, Chapter 4), and a dwarf is a "stripling" or "beardling" (Appendix A). (Elfling is also the name of a mailing list about Tolkien's languages, or elf linguistics.)
Some fans believe that Elves are vegetarian, with almost no evidence. The Hobbit Chapter 8, where the Elves of Mirkwood have 'roast meats', is one of several canon references to suggest that Elves do eat Meat.
In The Silmarillion Chapter 17, the Elves of Ossiriand say of Men: 'And these folk are hewers of the trees and hunters of beasts; therefore we are their unfriends, and if they will not depart then we shall inflict them in all ways that we can.' This suggests that Men eat meat but Elves do not, but there are other interpretations. Perhaps the Elves eat meat but fear Men competing for game. Perhaps the Elves eat fish, not beasts of land. Perhaps the Elves of Ossiriand are vegetarians but other Elves are not.
More recently, the movie of The Hobbit: An Unexpected Journey (2013) has a scene where the Elves of Rivendell serve no meat to the Dwarves. But this is not in the book.
Orcs in fan fiction like to ravish elven and mortal women. The canon never mentions sexual assault, so we can only guess whether Orcs would rape other races.
Minas Tirith, the city of seven circles, is where the wealthy live closer to the castle, while the lower and outer levels attract poorer and rougher folk. This is how The Games of the Gods depicted the city. This is only a guess, but perhaps a good guess.
Aragorn was orphaned at two. This is downright contradicted by the Appendices to LOTR: Aragorn's father died when he was two, but his mother lived until he was in his seventies.
It's also very, very commonly accepted that Aragorn and Legolas knew each other well before The Fellowship of the Ring took place. It's everything but canon now. Does make sense when you consider the facts though: Elrond and Thranduil most likely keep very close contact, and so given he's Thranduil's son, this would mean Legolas has probably spent a decent amount of time in Rivendell, where Aragorn has lived most of his life up to the Fellowship.
Boromir is a He-Man Woman Hater or even a Straw Misogynist. He thinks that women can't do anything. In fan fiction, Boromir acts rude to any woman he meets; and if the woman offers to help the group, Boromir argues against her. Fans do this to make their female characters seem more special.
Elladan and Elrohir are troublemakers. Elrohir is the more sensitive of the two, and Elladan has more of a temper. None of that is in the books.
Elrond was the romantic partner of Gil-galad, the last High King. Canon has no gay romance, but leaves enough room for one. Their romance would explain why Gil-galad gave the ring Vilya to Elrond, and why Gil-galad had no children to become High King after him. Also, Gil-galad died at the end of the Second Age, and Elrond did not marry Celebrían until the Third Age. This isn't enough to prove that their love was romantic instead of just platonic.
Erestor is the grim headmaster type in Rivendell. That's not in the books. He is only "Lord Erestor" in fan fiction. Erestor in canon is "the chief" among "counsellors of Elrond's household" (LotR Book II, Chapter 2). Fans also ship Erestor with Glorfindel.
Figwit or Melpomaen is not in the books. His names are Fan Nicknames for a background character in Peter Jackson's movies of The Lord of the Rings.
The idea that Glorfindel of The Silmarillion and Glorfindel of The Lord of the Rings comes from Tolkien himself, so it is canon! Tolkien wrote in an essay (found in The Peoples Of Middle Earth) that after Glorfindel died in The Silmarillion, he came Back from the Dead before The Lord of the Rings. To reduce Continuity Snarls, some fans omit essays like that one from continuity. This allows that the two Glorfindels are two different elves.
Glorfindel of Rivendell is only "Lord Glorfindel" in fan fiction. This might work if Glorfindel kept his title from the The Silmarillion and if anyone remembered his old rank. The problem here is that everyone in The Lord of the Rings seems to have forgotten about Glorfindel's title. He was "chief of the House of the Golden Flower of Gondolin" (Silm Chapter 23).
Legolas, for many fans, is the eldest son of Thranduil, and the next king after Thranduil. Legolas is an only child or has a younger sister. Canon never mentions any children of Thranduil other than Legolas, but they might still exist. A few fan stories suppose that Legolas has an older brother, which is not against canon.
The mother of Legolas (and wife of Thranduil) died before The Lord of the Rings. This idea is common, though each fan story gives a different version of her death. The Games of the Gods, Book One, Chapter 75, defies this idea by declaring, "yep, she was still alive".
What hair color has Legolas? Peter Jackson's adaptation of The Lord of the Rings might have settled the fan arguments. He's blond. The books make only vague references to his hair color. In The Hobbit, the Elvenking has gold hair. This king is Thranduil, father of Legolas; so it is plausible that Legolas inherited gold hair. The Lord of the Rings puts that most elves have dark hair, but is vague about Legolas. Some fans still believe that movie Legolas and book Legolas have different hair colors; the authors of The Games of the Gods, I Am Not A Mary Sue and What Grace Has Given Me defy the movie and write that Legolas has dark hair.
Morgoth, in many fan portrayals, simply looks like a bigger version of Sauron's physical form the Peter Jackson films. That's because Jackson used illustrator John Howe's Morgoth for movie Sauron. Howe was also hired for movie concept art.
Radagast has his name in the books, but never appears in them. Fans take his character traits from Peter Jackson's films of The Hobbit, where Radagast does appear.
Tauriel is not in the books. She comes from Peter Jackson's films of The Hobbit.
Thranduil is apparently an alcoholic who regularly beats Legolas senseless. This is highly unlikely, based on what we know of elves in general (elves have great difficulty even getting drunk, let alone addicted) and Legolas in particular.