WARNING!
UNMARKED GAMES ENDINGS SPOILERS AHEAD!
If you haven't played the games and/or seen all the endings, DO NOT PROCEED!
(partly because you won't understand a thing)
Talked to a staff member, and outright giving a warning beforehand is better than trying to cover everything in spoiler tags.
Now, the reason why I want to talk about endings is because I'm highly amused whenever anyone tries to claim that one route or ending is canon over any other. Why? Because if you actually look at endings themselves, there are barely any conflicts between them, and many don't actually need their respective routes to be the one and only canon route. Actually, I've been thinking about it, and in many games all good endings fit together quite well. So, what follows is my take on how all endings could have happened. It's just one way to look at them, some parts may be obvious, some parts might be just my speculation. But it shows that there's no need to choose any single route as the one and only way the stories could have happened.
One thing than needs to be reiterated before starting is that endings could have happened without their respective routes happening 100% as they're shown in-game. As far as routes go, I do agree it's safe to assume that Reimu had a major role in solving all incidents, but it's also possible that other playable heroines had a hand in it, from just going along for the ride to lending a hand on occasion to solving the incident side-by-side with her. How routes actually happened is another topic, though, and it's irrelevant to current one. Here, I'll just look at how all endings could've happened regardless of who actually solved the incident.
I'll do more standard games first, and then will look into versus games, since for those it also makes sense to show that all their routes happened as well.
Embodiment of Scarlet DevilNo conflicts here. The endings can be seen as independent, but they also fit into events of a single day nicely. The order would be MarisaB (Sakuya discovers her, Remilia leaves for the shrine), ReimuA (Remilia comes to the shrine), ReimuB (Remilia's already at the shrine), MarisaA (Sakuya serves her a meal, Remilia comes in). Supporting this being the same day is the fact that Remilia goes alone, which seems unusual.
Perfect Cherry BlossomThe endings can be seen as independent here as well, but some connections can be made. Both ReimuA and SakuyaB have Youmu being forced with cleaning duty, and she ponders it in MarisaB. ReimuB has Yuyuko and Youmu come to the shrine, with Reimu asking why. This could easily lead to a flower-viewing party in SakuyaB (not ReimuA because Marisa isn't present). In SakuyaA, Remilia isn't aware about Netherworld, so it's probably before she meets Yuyuko and Youmu. Lastly, MarisaA has her staying too long in Netherworld, so it's probably right after the incident. So the order of endings is probably MarisaA - SakuyaA - ReimuB - SakuyaB - ReimuA - MarisaB.
Imperishable NightFirst off, "Normal" endings. All of them result in heroines trying again after the fake full moon hanging in the sky for days. Even humans would notice that, but there's no mention of it anywhere. Plus there'd need to be another "Eternal Night Incident", or encounter with Kaguya would be much more different. And since restoring the true moon was kinda the whole point, it makes no sense for the heroines to ignore it for so long before trying again. No matter how I look at it, they're just glorified bad endings, and didn't happen as far as I'm concerned. Except one event - Yuyuko pestering Youmu to make pickles. It's alluded to in SWR, in a random Youmu vs Yuyuko quote, so such event probably happened after all at some other point in time.
Now, the good endings are completely independent. Only one of them requires for the respective team to reach FinalB - Netherworld Team's, since that's how Youmu got a case of red eyes (and insanity). Others only need the girls to know about Eientei crew. As I said, it's not necessary that only one route is canon, a few teams might've actually operated together. Also, I can definitely say that Scarlet Team's good ending happened because
this is the direct result of it. As for Reimu and Marisa, they probably know about Eientei because they also reach it when stage 4 ends even if they're bosses.
Why is everything involving Lunarians so complicated?
Mountain of FaithWith some assumptions, all endings nicely fit into a linear sequence: MarisaC (introduces Kanako to Reimu; only makes sense if Marisa went alone, so possibly not canon, not that it makes a difference), ReimuA (introduces mountain youkai to Kanako), MarisaA (mountain youkai already have a deal with Kanako), ReimuB (Sanae offers advice), ReimuC (makes a small shrine), MarisaB (makes her own small shrine).
Subterranean AnimismThe endings are completely independent, but if we assume that all partners somehow had a hand in the adventure, all endings could've happened independently.
Undefined Fantastic ObjectAnother one where endings can actually fit together. Byakuren decides to build a temple in ReimuB, and Kanako helps her in SanaeA. Since ReimuA and MarisaA have the ship flying around, they'd take place before that. In ReimuA, Byakuren is just happy to fly around freely so it's probably the first. Suwako visits them sometime while they're still flying in SanaeB. MarisaB doesn't depend on the ship itself and ties to the Extra stage, so it's probably the last. So the order would be ReimuA - MarisaA - SanaeB - ReimuB - SanaeA - MarisaB.
Great Fairy WarsAll endings fit into a single sequence: B-2 (Cirno introduces herself to Three Fairies before their flower viewing), C-2 (they throw a party for her), A-2 (Cirno tries leading them), B-1 (they prank Reimu together), A-1 (Cirno tries to show off during a flower viewing), C-1 (Cirno tries to pick a fight, leads into Extra stage).
Ten DesiresAll endings are independent and could've happened if all girls took part in solving it. There's a bit of a conflict in Reimu's ending in her conversation with Marisa, but the whole conversation can be ignored. Marisa also needs to be there at the end.
Double Dealing CharacterIf we assume that Marisa and Sakuya did use their weapons, they were still a bit crazy right after the final battle, so MarisaA and SakuyaA happened first. Eventually, the weapons would be back to normal anyway, and their "B" endings could still happen. SakuyaB would be first (since Shinmyoumaru wasn't present yet), then MarisaB (she brings Reimu Shinmyoumaru and the Mallet). Then it would be ReimuB (she tries using the Mallet) and in the end ReimuA (she decided to give shelter to Shinmyoumaru, probably after seeing she's no threat). Some endind details might need tweaking, but otherwise they may still fit together.
Fun fact for those who'd still insist on having just one route/ending, WaHH chapter 19 quite heavily implies Reimu did use her rod, so it's ReimuA if anything. Also fits with Shinmyoumaru living in a box in FS chapter 12.
Now, for the versus games.
Immaterial and Missing PowerThe only big indication about the order of routes that we have is the order of Suika's battles. If we assume her battles happened at the end of each characters' storylines, the order would be Sakuya, Alice, Youmu, Patchouli, Marisa, Remilia and Reimu. Their endings could happen anytime after Suika is exposed. Since Suika defeats everyone, and since Yukari's story straight up depends on exposing Suika, she's probably the last one to fight her and wins. Yuyuko remains a wildcard with her story possibly taking place anytime, but since it's Yuyuko, hers is probably before everyone else's (and she also wins).
Phantasmagoria of Flower ViewAlmost all routes and endings could've happened at the same time. The only exceptions are Komachi's and Eiki's, that are explicitly after everyone else's, and Yuuka's, which is before Reimu's. Also, Tewi's, Reisen's and Medicine's probably took place in that order. Reisen tells Eirin about Medicine's field in her own ending, and they come there in Medicine's. Tewi is affected by Medicine's poison, but it seems neither Reisen nor Eirin recognize that.
Scarlet Weather RhapsodyThis thing describes everything and I have nothing to add. Huge props to whoever worked on it.
HisoutensokuThe three stories are largely independent and have only a few common points. Cirno vs Sanae happened first, Cirno goes to Utsuho right away while Sanae goes to SDM and visits Utsuho later. Meiling's story happens after her fight with Sanae.
Hopeless MasqueradeI haven't played this one, so I'm going by summaries on the wiki. It's known that Mamizou's and then Kokoro's stories happened last. Kokoro gets a permanent new mask in Koishi's ending, so it's probably right before them. Only Ichirin and Futo can't help Kokoro with her mask, so their stories are probably before everyone else's. All other stories take place either simultaneously or close to each other.
Well, that should be it. If anyone has anything to add or point out (or wants to share a different theory that isn't baseless nonsense), feel free to post it.