Every fan knows that Zelda transformed into a male in the The Legend of Zelda: Ocarina of Time manga. It is constantly used as "proof" that Sheik in the game is a Gender Bender instead of a Sweet Polly Oliver. Despite this belief, it is not true. The only "proof" is that Ruto called Sheik a man. The manga implies that Sheik is mainly a case of crossdressing, with magic changes being limited to aesthetics like hair length and eye color. Sheik wears a sarashi, covers up their face, keeps their distance from others, and keeps encounters with Link limited. When Link carries Sheik in one scene he notes that they're surprisingly light. Ruto calling Sheik male is simply due to Ruto not realizing otherwise. Sheik is male in the manga, mentally at least, as Zelda's personality was locked away and replaced with a male personality. This is non-canon to the games, which make it clear that Zelda was is in control the entire time.
The idea that the series has no continuity or plotline, and is simply the same tale each time. In reality, even ignoring the series' complicated timeline, there have been direct sequels to individual plots. Games like Twilight Princess and Spirit Tracks have included more and more references to earlier games, indicating Nintendo is aware of this criticism.
"Link" is not a singular character, nor is Zelda. There have been many Links (who may or may not be related) and many Zeldas (who are all part of the same royal line note Thanks to the split timeline, there's technically three lines, but they're all descended from Ocarina of Time Zelda). Only Ganon(dorf) usually remains the same person from game to game. There is actually one confirmed instance of Ganondorf not being the same: The Legend of Zelda: Four Swords Adventures, which is in the Twilight Princess timeline. Several hundred years after Twilight Princess he is born again in the Gerudo tribe, with no memories of his past life. You will anger the fans if you assume Zelda and Link are same characters in each game.
Word of God is that the individual heroes of each game may not actually be named Link. As the series' title suggests, the games are legends—meaning that they were passed down many, many generations after they happened. It's possible that each character we know as "Link" had their own name which was retroactively changed to "Link" by future storytellers. This is not true for Zelda or Ganon, however; every princess named Zelda actually had that name, and Ganon is usually the same exact person.
Only a few Zelda games thus far are more-or-less direct sequels to another with the same version of Link: Zelda II: The Adventure of Link, which states that the blood of Link must be sprinkled onto the ashes of Ganon (which was his final state at the end of the first game) to resurrect him; Phantom Hourglass is a sequel to Wind Waker (Spirit Tracks is also a direct sequel to that, with Niko being the same character in all three games, but the Link is different); and Majora's Mask to Ocarina of Time. A Link To The Past has Link's Awakening and A Link Between Worlds; however, the former is largely unaffiliated to ALTTP and the latter takes place generations later.
A lot of people seem to be under the impression that the multiplayer modes of Four Swords and Four Swords Adventures require four players (probably because of the title). In actuality they can be played with two or three people as well. So you don't have to worry about having to buy four GBA systems and cables if you only really want to play in a two or three player game. And Adventures can even be played single-player; so can the DSi port of Four Swords.
There's the impression that Link found Navi annoying or hated her. While it's true that many players hate Navi, Link actually valued her as a true friend and cherished her companionship, and it's implied that the "friend" that Link is mentioned to be searching for at the beginning of Majora's Mask is Navi.
Players hating Navi is because of a misconception, since many believe that she constantly nags you to get back on track with the plot every five seconds. Actually, her reminders come about every 10-20 minutes real time, and she doesn't force you to view them. She doesn't say "Hey, listen!" as one line either - she says "Hey!" when she has something to tell you, then something else when you press the C-Up button to talk to her - "Look!" when pointing something out, "Listen!" when reminding you what you were supposed to be doing, and "Watch out!" when giving advice on an enemy.
Everyone knows Dead Hand is the horrifying boss of Ocarina of Time's Bottom of the Well dungeon. Well, yes, but it'd be more accurate to say he's a miniboss in the Bottom of the Well, which is mostly optional and has no climax, being a mini-dungeon you only have to enter for the Lens of Truth. The Dead Hand can be fought almost immediately after entering, and after claiming the Lens of Truth (which it guards), you can leave at any time, with rewards there to be found but no scripted sequence of events there. The earlier Ice Cavern mini-dungeon was linear in nature, so the miniboss was more of a climax there. Also, there's two Dead Hands in the game, with the other guarding a room in the Shadow Temple afterward, but almost nobody reminiscing on the Dead Hand mentions that there's a second one.
People saying that Link is incapable of talking. He can talk, and it's implied that he is responding to NPCs, we just don't hear his replies (for instance, it's implied he says his name when someone asks it), and the player is supposed to imagine how he'd respond because he's supposed to be an extension of them. Occasionally he speaks in the form of player-chosen responses. In the manga adaptations of the games, he talks all the time, and in Wind Waker he occasionally shouts "Come on!" (the only time in ANY game where he says actual words in voice rather than in text). Breath of the Wild takes this even further, with some more personality-driven dialogue options that NPCs will react to like Link said them just as written.
Link in The Legend of Zelda: A Link to the Past does not have pink hair. His hair was pink due to issues with getting the palette to work on the Super Nintendo. All official art clearly has him with a dark blond color.
On a similar note, many fans think Zelda and Link are consistently blond. This is incorrect as the NES Link is a brunet, the first Zelda was a brunette, and the second Zelda (the Sleeping Zelda) is a redhead. It wasn't until A Link To The Past that blond became the staple. On the other side of the spectrum, the A Link to the Past Link (and others using the design), Twilight Princess Zelda, Twilight Princess Link, and Skyward Sword Link do not have brown hair, but dark blond hair.
Link being an adult in his older designs is this. So far no Link has been shown above eighteen, the Age of Majority in many modern countries. The oldest Link is only seventeen and even if he was eighteen he'd just barely be an adult.
Some fans firmly classify Zelda games as RPG, while they are actually Action-Adventure (the only one to have any RPG elements at all is Zelda II, which is otherwise a side-scrolling action game). The question of whether the series is an RPG is a common way to start arguments.
A lot of non-fans and media claim that Link's task in all the games is to Save the Princess. While this is true in a few games, it is very much not the case for all of them - most of the time, Zelda either doesn't appear at all in a game, or takes a fairly "backseat" role, and some games even have her working together with Link.
Link is not an elf. His long (and that's specifically long, since all Kokiri have pointy ears) pointy ears indicate that he has Hylian ancestry.
A large number of fans believe every Link and Zelda are a reincarnation of the first two from Skyward Sword. This is actually not entirely true. The "Sleeping Zelda" from Zelda II: The Adventure of Link does not contain the spirit of Hylia. She is simply the princess who started the tradition of all Hyrulian princess' being named "Zelda", as tribute to her. The one who contains the spirit at that point was the Zelda from the original game, who co-exists with her but doesn't actually appear in the game.
In the first game, the method of defeating Ganon was a mystery that the player had to unravel (or learn through word-of-mouth), but turned out to be two direct hits from a Silver Arrow (after striking him with a sword to turn him visible). This factoid was turned into a recurring plot point on The Legend of Zelda show that aired in the 80s, where Link already knew he needed to get two hits on Ganon to finish him off for good but could only ever land the first one before Ganon made an Exit Villain Stage Left. However, unlike in the games, his sword (or its beams) seemed to work fine for that purpose.
Link's infamous Vai Gerudo outfit in The Legend of Zelda: Breath of the Wild is commonly assumed to be an outfit he never took seriously or wore to be cute, with the optional male outfit being the one he wore when doing serious work in the Highlands. This actually reverses the relevance both outfits have: the Vai outfit is the one he needs to take seriously, as it was the only way to sneak into Gerudo Town without raising suspicion. It's the Voe outfit that's the fetishistic one, as he obtained it from a hidden group of crossdressing Gerudo women.
Hyrulean and Hylian are not the same thing. "Hyrulean" refers to a resident of Hyrule while "Hylian" refers to a race of long-eared people. Not all Hyruleans are Hylian and it's theoretically possible for a Hylian not to be Hyrulean, though the games only focus on Hyrule so this isn't explored.