Ascended Fanon: Quite a lot of it, though all ascended fanon is usually a coincidence as ZUN has said he doesn't look at fan games because he doesn't want to plagiarize, unintentionally or on purpose.
Much like with Daiyousei and Koakuma receiving fan-names, Momiji makes a cameo appearance in one panel of Oriental Sacred Place Chapter 1, looking exactly the way fanon imagines her, with wolf ears and detached sleeves, though some recent official art showed her apparently without wolf ears. The artist for Strange and Bright Nature Deity and Oriental Sacred Place was a Touhou fan doing doujinshi long before being recruited for the official project.
Though Daiyousei never got official art from ZUN, she has a probable cameo in one chapter of Strange and Bright Nature Deity looking and acting very much the way fan art tends to portray her, with the distinctive side ponytail. However, her Fairy Wars sprite, being based on the EoSD one, lacks it.
In addition to the fan-given name, Koakuma had a cameo appearance in Inaba of the Moon & Inaba of the Earth with two pairs of black wings, one on her head and one on her back, just as depicted in fan art.
Because of her connection with history, her home in the human village, and a comment by Remilia, Keine was frequently cast as a teacher to other characters in fan works after Imperishable Night. Later official works made this canon (though it jossed the idea of her teaching any youkai characters, since she said she only wants to teach humans).
Apparently things like this were even happening in the PC-98 days, since ZUN hangs a lampshade on it in the manual for Embodiment of Scarlet Devil.
Unintentionally, [Reimu] is a shrine maiden. Or rather, she is a shrine maiden only because the Touhou series has become the "Shrine Maiden Shooting Game" series. It feels like the cart has been placed before the horse to me.
Hopeless Masquerade has made quite a few fanon ideas canon, such as Marisa surfing on her broom and Mamizou smoking a pipe.
Chapter 21 of Wild and Horned Hermit depicts Sakuya wearing a pinstripe coat and lacy headdress, making her look almost exactly like she does in Koumajou Densetsu.
Beam Me Up, Scotty!: The loading screen quote at the top of the Main page is often misquoted as "wait warmly" instead of "watch warmly".
Cowboy Bebop at His Computer: Special mention to CNN, who covered the Shadow Art PV for Alstroemeria's "Bad Apple!!" with little to no idea of what they were actually talking about. They even went so far as to say that the stop-motion version was the origin of the entire thing, making this a Critical Research Failure. This incident led a number of Touhou fans to refer to CNN as the "Cirno News Network".
Hong Meiling - China is so widespread that even ZUN has admitted to using it. Before that it was Kurenai Misuzu, the Japanese pronunciation of the Chinese characters that make up her name. An ongoing debate over whether her name was supposed to use the Chinese or Japanese pronunciation was, in fact, the source of the "China" nickname, which was offered as a compromise because being Chinese was her main identifying trait anyway. It's used less and less often these days, now that Meiling is more of an established character.
Part of the origin of her nickname was that it was a joke on how Chinese things are unreliable, referencing her exaggerated napping status. Part of the reason it's being used less is because many fans don't care for that treatment of her.
This nickname is so strongly associated with her that "China" redirects to her page on the Touhou wiki.
Sakuya - PAD-Chou/Pad Chief. Fans noticed her bust size change considerably between her character art in Embodiment of Scarlet Devil and Immaterial and Missing Power. While this is probably because the former's art was done by ZUN, who many believe simply isn't good enough at perspective to draw breasts, the tongue-in-cheek fan theory that she started padding her bra between the two games caught on. Fanon has it that mentioning such in her presence is a good way to wind up knifed to death. She's also called Sakuya Brando due to her similarities to Dio Brando. This really says it all.
Yuuka - Japanese fans often call her Yuukarin as a take on Yukari's Yukarin. Yuuka can also be romanized as Yuka, though, so the distinction is often lost in English. She's also sometimes called Ultimate Sadistic Creature, or USC for short, due to some of her lines suggesting that she enjoys dealing out violence. Youkai Moenote A pun: the literal meaning of moe is "budding", and she's a flower youkai is sometimes used with her.
Kogasa- 2nd or New Youkai Moe.
Merlin - Meruponote a combination of her name and "nurupo", short for "null pointer exception" (a programming term), in reference to her occasionally buggy behaviour in Perfect Cherry Blossom, also known as ξ・∀・
Lunasa- Luna-nee, reflecting her "responsible oldest sister" position among them.
Youmu's is referred to as Myon among fandom due to a quote of hers from Perfect Cherry Blossom. Western fandom has applied this specifically as a nickname for her ghost half.
Ran - Suppa-Tenko, translated as "Naked Heaven-Fox", from an infamous fan-comic. Because of this, some fan works often humorously portray her as a streaker.
Yukari - Yukarin, also Sukima ("gap"), in reference to how her powers manifest, and Babaa ("old hag") in reference to her extreme age. This would be 1300 years old minimum, as she created Gensoukyou and is thus one of the oldest characters in a series filled with centuries-old characters.
Suika - Watermelon. Her name is a homophone for the Japanese word for the fruit. It is rumoured that the origin of watermelon is related to Suika as well.
Reisen's bullets were probably just intended to look like they're glowing, but the fact that most of them in Imperishable Night are colored white caused some fans to speculate that they're suppositories. The name stuck, due in no small part to another flash byIOSYS, so some call her "Suppository".
Kaguya - NEET. In Fanon, Mokou also uses this as an insult, although Kaguya has taken to rebutting by calling her a hobo. Also Teruyo, an intentional misreading of the kanji that make up her name. Naturally, it gets more use in Japan than the western world.
Aya - "Slut", or "ZUN's girlfriend". Detractors of her Creator's Pet tendencies sometimes jokingly suggest that she seduced ZUN to secure her spot in nearly every Touhou game after her debut, not to mention those spotlight-grabbing Gaiden Games and her generally high power level. It also doesn't help that ZUN once wore an outfit matching hers.◊ It has fallen out of use these days for the most part, due to more characters being introduced that have taken prominence over her.
Eiki - Yamada, a pun about her position as Yama ("Yama da" meaning "it's the Yama") and the common Japanese surname Yamada.
Komachi- Komachichi, a Pixiv-made nickname referencing her two most noticeable Traits
Kanako - Guncannon, because of a spell card of hers that attaches pillars to her shoulders. Kanako's breasts, due to their large size in most fan depictions, have a Fan Nickname of their own: "Mountains of Faith".
Suwako - Western fans often call her Suwacko or Swackers, while her Nice Hat is known as Pyonta. Also "Kero-chan" (Froggy), derived from her Native God "Kero-chan Braves the Wind and Rain" spell card.
Iku - 193 (ichi kyuu san -> Iku-san). This occasionally leads to crossovers with Kamen Rider Kiva, where IXA is read similarly.
Tenshi - Chiquita Dragonforce, Peaches and Momoko due to the fruit in her hat. Tenko, an alternate reading of the kanji in her name, is both used as a nickname for her and as a means for linking her to Ran's Suppa-Tenko meme.
Kisume - Bucket Ranka, because of her resemblance to a certain Macross Frontier character. Otherwise, she's known as Bucket Loli.
Parsee: Known in some circles as "Cave Alice," for her visual similarity to Alice Margatroid and for... well, living underground.
Utsuho - Chernobyl-tan, due to her nuclear fusion powers; Bahamuko, from Bahamut of Final Fantasy fame due to her spell cards titled "Mega Flare" and "Giga Flare"; Onric or "⑥", due to being similar, yet opposite to Cirno; and finally Deep Crow. Many use the in-game nickname Okuu.
Ichirin - Due to the way Unzan supports her in combat like a Stand, a noticeable number of fans have begun calling her Ichirin Kujo. Cue the fist-versus-knife-fight with Sakuya. Less flatteringly, she's also called Unzan's Hitboxnote after an awkward comment by ZUN in an interview, saying that Ichirin only existed so Unzan would have a hitbox.
Byakuren - Youkai Jesus, Youchrist, Gensoukyou Gandhi, Suigintouhou and The Anti-Marisa, because she is a magician and is an opponent who pillages patterns from Shinki, Yukari, Yuyuko and Marisa herself.
Nue - U.F. Owen, due to her supposed similarities to Flandre and her UFO-themed spell cards.
Unnamed Giant Catfish - Primeus, in a reference to a M.U.G.E.N joke character of that name made by Ricepigeon, to the point that some people actually think that's its name. More recently, people have taken to calling it Namazu, which is just the name of its species. This is somewhat justified by the fact that it is referred to as "namazu" in the game's files.
Reisen II, for the moon rabbit introduced in SSiB, to differentiate her from Reisen Udongein Inaba.
Yorihime - Moonbitch, as popularized by her detractors, though her name being hard to remember didn't help her. Both Watatsukis together (or, more rarely, all Lunarians) can also be referred to as "the moonbitches", but the singular "Moonbitch" seems to be Yorihime. She and her sister are sometimes called Moonsues, due to their Nigh-Mary Sue status.
Several unnamed characters have officially adopted their Fan Nicknames, like Tokiko, Daiyousei and Koakumanote Usually shortened to Dai-chan and Koa, respectively.
Mamizou and Nue, together, are for some reason being labeled "The Frat Boys".
Meaningful Release Date: The English patch for Yousei Daisensou was released on September 9. The game stars Cirno, who has a memetic association with the number 9.
Nintendo Hard: Double Spoiler, is somewhat better thanks to improved camera controls and a new unlockable character that makes most cards easier to beat. It's still harder than the normal Touhou games, though. ZUN even had this on his blog.
This is true for for Shoot the Bullet and Great Fairy Wars, because of the ability to clear bullets more freely compared to normal entries.
No Export for You: Zun expressed he is not willing to sell to western audiences. Supposedly, this is mostly due to shipping costs and the potential for cultural misunderstanding (Ran's swastika spellcards were cited as an example.)
It seems some people believe that he doesn't want people selling it via "downloads aimed at overseas buyers", either, according to the official Touhou Project Guidelines. However, this is due to a mistranslation; the original guidelines are clearly labelled as applying to fanworks based on the Touhou series, and state that such works shouldn't be sold via the App Store, Android Market, Xbox Live or downloads aimed at overseas buyers. Of course, this isn't happening.
ZUN changed his mind over time; at Anime Weekend Atlanta 2013, he said he was interested in bringing the franchise to the US, and specifically mentioned that he liked Steam as a possible avenue for distribution. However, he said the biggest issue was that someone else would have to do the translation, and he really preferred being able to handle the games from start to finish. In March 2014, he officially announced his intention to digitally distribute the games for an international audience.
Sleeper Hit: Even the fandom is baffled at how a simple shooting game series got so popular.
Trolling Creator: When SOPM came out, a lot of the profiles subverted the moe treatment many characters got (Nitori is not a shy kappa, she's a racist asshole, Hina is not someone you want to be near), and in the interviews following after, ZUN claimed Kisume - another shy youkai - is a Serial Killer who decapitates people and throws skulls at others and that Tenshi was misunderstood and bullied by everyone. In case anyone doubted what SOPM had to say about Nitori, her dialogue in Hopeless Masquerade is extremely different from her dialogue in Mountain of Faith (and even Subterranean Animism, where she encourages the player to beat up their opponents), which consists of insulting her opponents and openly bragging about being a scammer. The only person she isn't mean to who isn't a customer is Marisa, her old comrade, and even then it's pretty neutral.
Though the Kisume remark was made loosely (likely as a joke, not definitive Word of God), and while So PM's articles written by Akyuu might be questionable, Hopeless Masquerade supports some of it.
ZUN did this a bit earlier with sinking the popular fanon ship of Aya and Momiji in Aya's notes for Double Spoiler: Momiji really dislikes Aya. Not that this has stopped fanon.
Mokou's popular portrayal of being a vengeful, tsundere rageaholic obsessed with Kaguya was upended in Cage in Lunatic Runagate, where Mokou admits she actually forgot about Kaguya until recently and only fights with her out of boredom. She's also much less angry - more like an apathetic, quiet slacker who hangs around in the forest.
Though her chapter does show the notion of Kaguya leaving is greatly upsetting.
What Could Have Been: Byakuren wasn't the original intended final boss of UFO; her brother Myouren was the planned final boss instead. However, ZUN didn't want players to beat up an old man, and having a lone male in an overwhelmingly female cast would have been too jarring, so Myouren was relegated to Byakuren's backstory.
ZUN had been thinking of making a team-up game (which later became Imperishable Night) before the Windows games even came out. EoSD was originally supposed to be the team-up game, but ZUN felt it would be odd to have sets of previously unintroduced characters be playable. EoSD and PCB were then made to introduce the player to several sets of new characters in preparation for IN.
Shoot The Bullet was a game he'd had an idea for since the time of Eo SD, but it wasn't until Aya came along that he could really make it—that, and a collection of otherwise impossible-to-beat spell cards.
When Embodiment of Scarlet Devil introduced the spell card system, it became the first shooting game ever to give an official name to one of its bullet patterns. (Naturally, some patterns are given names by the fans. Touhou itself has "Gengetsu Rape Time", after all.)
However, this has caused some speculation on the nature of things before them, sometimes reaching Fan Dumb levels.
Nonstandard boss fights:
Alice in Perfect Cherry Blossom appears twice as a mid-boss (the first after only a single wave of fairies) before the full boss fight later on.
Mystia in Imperishable Night starts her boss fight immediately after losing as a mid-boss.
Kanako's stage in Mountain of Faith has no mid-boss at all.
Miko's stage in Ten Desires follows the same trend.
Yuugi in Subterranean Animism stays on the screen after mid-boss fight and continues shooting at you.
Nue, the extra stage boss in Undefined Fantastic Object, appears as the mid-boss in Stages 4 and 6, but in the form of a ball of light.
Rin, the Stage 5 boss in Subterranean Animism, is a mid-boss in Stage 4 (twice), Stage 5, and Stage 6. She's infamous for her persistence.
Byakuren Hijiri, the final boss of UFO, has no hitbox.
Soga no Tojiko, the stage 5 mid-boss in Ten Desires does the same thing.
Kurumi in Lotus Land Story was the only PC-98 character to act as her own mid-boss. The Windows games made this the standard.