Only Touhou games, CDs and literature produced with ZUN's involvement are considered to be official canon for the Touhou universe. These are listed under Games, Print Works and Music on the main page.
Uncertain canonicity of PC-98 and Seihou games
Even among ZUN's works, the canonicity of the first five Touhou games produced for the PC-98 platform is uncertain, because in the Windows games, events from the PC-98 series were only vaguely mentioned twice, by Alice in PCB and by Reimu in PoFV, in Yuuka's scenario. The only characters from the PC-98 games to appear in the Windows games are Reimu, Marisa, Alice and Yuuka, and except for Yuuka but especially for Reimu, the Windows versions of their character designs have looked significantly different from the PC-98 versions. There is no canonical explanation for these changes in appearance; theories such as PC-98 Reimu being the mother of Windows Reimu are fan speculation. No references have been made to any other PC-98 characters since the Windows series started with Embodiment of Scarlet Devil. For example, it is unknown whether Mima and Ruukoto are still living at the Hakurei Shrine, but they have been depicted doing so in a few doujinshi.
There is a possible reference made to Mima in Curiosities of Lotus Asia Chapter 25, where Reimu comments that the Hakurei Shrine was once taken over by an evil spirit for its god (something that Mima, an evil spirit, did). The fact that Mima isn't mentioned by name, however, might mean this is just an Easter egg continuity nod (or possibly discontinuity nod, considering Reimu's comments about there being no records from that time) instead of any confirmation of canon. Another possible reference is made to Genjii, whom ZUN mentioned in an interview is "probably living in the lake at the back of the shrine", in Strange and Bright Nature Deity Chapter 12. When Reimu and Marisa were talking about "glowing moss", Reimu said it would be nice to transfer it to the pond in the back of the Shrine and Marisa responds that she could make it grow there on the turtles' backs. It's possible that one of them is Genjii out of those turtles.
The appearances of some Touhou characters in the Seihou games may probably not be canon, since there are no references to them in Touhou works. However, the accompanying story text to Reimu's theme in Shuusou Gyoku, which was included in ZUN's Dolls in Pseudo Paradise CD, mentions a girl that "doesn't look like a human or a youkai" heading to the shrine. This could be referring to VIVIT, who is neither of those and is a robot, heading to the shrine in her game's Extra stage.
Multiple playable routes
When games have multiple playable characters (PCs) advancing through the same levels, the question of which characters did what to resolve the incident becomes ambiguous. Many fans assume that Ending #1 in all games is what actually happened (although there is no proof to this other than the numbering), but if this is the case, then Reimu has won all of her fights except one, against Suika in Immaterial and Missing Power. Some fanworks assume that all of the PCs participated in the incident simultaneously, but fought different enemies at various times, the main priority among fan creators usually being to support the most popular character relationships. In Embodiment of Scarlet Devil, for instance, Reimu x Remilia, Marisa x Patchouli and Marisa x Flandre became the most popular pairings. Many fanmade reconstructions of the game's events therefore depict Reimu and Marisa traveling to the Scarlet Devil Mansion together, and then splitting up so that Marisa fought Patchouli, Reimu fought Remilia, and then Marisa fought Flandre sometime later in the Extra stage.
References in the dialogue and afterwords suggest that indeed all PCs set out to solve each game's incident, although in some games this is explicitly contradicted in the manual where it sometimes says, depending on which character you choose, only one goes out to investigate. Similarly, in Imperishable Night, only one youkai team and one human team are said to investigate.
In the case of Scarlet Weather Rhapsody, most of the PCs' storylines refer to events that happened in other PCs' storylines, making it very likely that all of its playable routes are canonical events occurring at the same time from different characters' points of view.
Fanworks, most of which consist of doujinshi and fanart, are non-canon. This includes the game Concealed the Conclusion, with its premise about the fundamental nature of Gensokyo, and the Touhou Project Side Story animated video, whose depiction of Lunarian civilization was contradicted by Silent Sinner in Blue a few months after the video's release. The fan comics included in the official fanbook Bohemian Archive in Japanese Red and the semi-official fanbook Seasonal Dream Vision should also be considered non-canon (with the exception of Extra of the Wind, which was written by ZUN), despite appearing together with some of ZUN's work.
Artists who produce both doujin and official work
ZUN collaborates with established Touhou doujinshi artists to illustrate his official print works. However, even if an artist has worked on an official Touhou project, other works by the same artist in which ZUN did not participate are non-canon. For example, Aki Eda is the artist for the official Touhou manga Silent Sinner in Blue, but the storylines she introduces in her self-produced doujinshi, such as the Alice x Patchouli pairing in the "Plastic Heart" series, should not be considered canon. Also note that, despite being considered an official Touhou work, the canonicity of Inaba of the Moon and Inaba of the Earth may be somewhat debatable, both due to its slightly over-the-top comedic gag nature, and due to ZUN reportedly being only loosely involved in its creation. However, due to the fact that some character relationships, like the one between Mokou and Kaguya, can be gleaned from Inaba of the Moon and Inaba of the Earth, it is still a good (if unreliable) source by which to gauge their relationship when compared to other doujin artists like Tohonifun.
There are hundreds of Touhou OC's (Original Characters) scattered around the internet. Most often they are ignored. Some fan-created characters, such as those in the following Danbooru listings, have become memes in Japanese (and in the case of Meimu, Chinese) Touhou fandom. They are popular enough to be drawn by multiple artists, but should definitely not be considered canon.
NSFW WARNING: The links to Danbooru contain hentai (adult related) ads and possibly adult images in the search. If you do not wish to see these ads or adult-rated pictures, proceed to the Safebooru links which contain no adult content. Danbooru tends to have more pictures than Safebooru, so please proceed with caution.
All material relating to yukkuris is also non-canon.
The canonicity of Rin Satsuki is ambiguous: as a character whom ZUN originally intended to include in Embodiment of Scarlet Devil but then deleted before the release of the game, she has never appeared or been referred to in any canon Touhou work. She has occasionally appeared in fanworks.
Fan artists may make non-canon speculations about the appearances of characters with no official artwork. For instance, many people assume that Myouren Hijiri had the same purple-to-brown gradient hair that his sister Byakuren does, but since he was a Buddhist monk, it's more likey that his head would have been shaven.