WMG / Kanon

Makoto cheats death, goes back in time and becomes the original Sawatari Makoto.
Mishio clearly states that the sacrifice that Makoto must give To Become Human is comprised of two parts: her memory and her life. However, Ayu creates a much, much stronger miracle, only loses a small fraction of her memory (whereas Makoto forgot her entire history), and lives to tell about it, even surviving a Really Dead Montage. So could it be that when we saw Makoto laying on a green, sunny Monomi Hill, it wasn't Yuuichi thinking about how he would revive her, but she really was back... somewhere? We know that Ayu's super-miracle fixed up the other girls' lives overnight, even when they seemed completely helpless. There's no reason to believe that she wouldn't be able to send Makoto back in time and return her to human form. There, knowing human customs and the history, she would be able to replace the original Sawatari Makoto (who may have died shortly after birth?) and live through that life. The 2006 version of the show plays with the idea; the real Sawatari Makoto is shown to look and sound like an older version of the one we know, with the same love of meat buns and bells, which is clearly stated to come from her fox side. Also, in the very end, a fox appears that looks just like Makoto's fox form. (Great, now I'm going to start believing this.)
  • Couldn't she just simply be resurrected at the beginning of spring to lead a normal life? They did make clear Yuichi names the fox after the real Makoto and all...
  • Or as another theory, Makoto really is dead, but deliberately took the form of a younger version of the woman she was named after, in order to get Yuuichi to like her (because she knew he liked Sawatari Makoto). Of course, this doesn't explain Sawatari Makoto's love of bells...

The entire series is Ayu's dream, up to the last few moments.
At the beginning of the third episode, Ayu's 'dream' monologue mentions, "How long has it been since I realized this was a dream? A few minutes, or much longer?" or something to that effect. In the immediately previous episode, when complaining about Yuuichi dodging her, she makes a point about emphasizing the "ruined drama". Ordinarily this would be just your run of the mill Fourth Wall busting, but think about it: all the fantastic things that happen to Yuuichi that can't happen in the real world, where the series is set, make perfect sense in the context of a dream. And the town is small enough that it would be unreasonable to think that all these girls (or animals or what have you) connected to Yuuichi would be completely unaware of each other's existence. This also answers why Akiko doesn't reveal the critical detail of Ayu's existence: in the "real" real world, she does. Almost immediately, in fact; subsequently, Yuuichi goes to the hospital to an awakening Ayu. The dream, therefore, is in the last few minutes of her coma, within a few days of Yuuichi coming to town.
  • But why would Ayu and Yuuichi get together at the end if he didn't experience the events from his perspective?
    • It's still possible (although I personally don't think this is the case): if the events from the audience's POV occurred within Ayu's dream, then Yuuichi's faulty memory may be just be a fiction that she projects to compensate for not knowing how he grew up. It's entirely reasonable for Yuuichi in the real world to keep the torch burning for his childhood friend in the interim; if he was informed on his arrival that Ayu was in hospital and not, as he had previously assumed, dead, he could have headed straight to the hospital to keep vigil until she woke up. Remember, it's not made explicit exactly how much time has passed between her recovery and what transpires towards the end of the last episode, so she could have made the acquaintance of the other girls during that unspecified period.
  • The town's not so small - the high school is large enough to easily get lost in, and when Yuuichi and Nayuki try to take a short cut and get lost, they don't get back to school until lunch time. (These comments are based on the game - I don't know if they apply to the anime.)

Most of the series is real, but the last few scenes (after Yuuichi finds the headband) are a dream.
The opposite of the WMG above, in other words. Ayu's supernatural dream lets her meet Yuuichi in the real world and heal several of his friends, but this dream fades out around the time Ayu vanishes (her background narration says the dream is ending at about this time). A somewhat depressing take on things, but it does explain a few oddities; mainly the blurred dreamlike appearance of much of the last few scenes, and the fact that Ayu could project a copy of herself into the physical world and magically heal a bunch of people, yet couldn't heal herself and seemingly thought Mai couldn't help her either (why would Ayu get better long after the people she healed, instead of at the same time? Invoked Rule of Drama?). The headband-giving scene could only be a dream of Yuuichi's (unless Time Travel is involved), which makes the following and final scene, with Ayu awake for no stated reason, all the more suspicious. She probably does wake up eventually—kinda hard for Yuuichi to "always be smiling" if his girlfriend's in a coma—but the way it's shown in the end seems ambiguous on purpose.

The reason that Akiko is so accepting of the Pretty Freeloaders is that she's was in Yuuichi's position when she was younger
At least one other person (Mishio Amano) has had similar experiences to Yuuichi so there's no reason that it couldn't have happened to others. Akiko just happens to be one of them. It logically follows that...

Nayuki's father is some sort of supernatural entity
We never see him because he's passed on, vanished, no longer able to take human form something.
  • This could explain Nayuki's obsession with cats, maybe he turned into a cat.
    • Nah, Nayuki loves all cute animals.

Yellow? Check. In a jar? Check. Adverse effects on anyone who comes in contact with it, including being powerful enough to even scare away a bunch of teen girls, even if they are powerful and very skilled fighters? Check.
  • No. Ew.

Yuichi is Kyon
This is probably what would've happened had Kyon of gone to a school other than North High. And then ran into a bunch of girls who had issues. I know, same voice actor, but his dialogue/sarcasm mode seems to fit both characters.

Mr. Minase was a fox.
We know that Akiko already knows about ikiryou from how she automatically understands Ayu's situation, but as CLANNAD proved, under normal circumstances (without a miracle like Ayu's), ikiryou are forgotten once discovered and proven (poor Fuuko), so he couldn't have been one of those. But Mai knew about ikiryou too, from her experience with other supernatural phenomena. Akiko is also unbelievably accepting of Makoto and understanding of her situation, doesn't question the ending of her route, and in the 2006 anime, breaks down crying after Yuuichi and Makoto leave the house for the last time, implying that she knows Makoto won't be coming back. We also know that there was at least one fox spirit before Makoto (see Mishio) and that there are likely to have been more (as Nayuki mentions that it's a legend around town). So, Nayuki's father was a fox, and he isn't around because he disappeared after sacrificing memory and life.
  • This troper reached the exact same conclusion independently. There is certainly a lot of logic behind this theory.

Mai was the demons.
She's been having severe psychological issues as a result of her very sad backstory. Any harm she did to herself or others was actually her own doing.

The pressure and stress of dancing in front of a crowd of people who were whispering to each other about her being a "troublemaker" caused her to have a nervous breakdown in the dance scene - there were no demons, she was just destroying the room.

For most of the series, the teenage Ayu is just an imaginary friend made up by Yuichi.
All of teenage Ayu’s appearances prior to the last episode of the series were just a fantasy created by Yuichi’s imagination, serving as a safety valve for his psyche at times when the hard reality of her apparent death is too much for him to keep completely suppressed and he needs an outlet. The rest of his friends are just humoring him and pretending to interact with the imaginary Ayu in the hopes that it may help him come to terms with the accident and eventually be able to help the real Ayu who's still in the hospital. This is why the imaginary Ayu still acts, talks, and looks like such a young girl despite being “seventeen,” since Yuichi’s basing his version of her on the ten year old that he knew while imperfectly projecting what she might physically look like as an older teenager. It's also why the imaginary Ayu doesn't appear on the days when Yuichi’s mind is completely focused on one of the other girls, why she knows all about a headband he never actually gave her yet doesn't even know she's wearing a winged backpack until he points it out, and why she is the only person offered Aunt Akiko’s jam who isn’t shown actually eating it (since playing out the whole scenario to completion would have required Yuichi to eat it himself).

Nayuki suffers from Split Personality.
One part of her is upbeat, cheerful and athletic, another part is sad and depressed, so she sleeps a lot to suppress any emotional trauma she suffers, such as when Yuuichi rejected her love confession seven years ago, or when her mom Akiko suffered that car accident.
Further evidence is that, in the doujin Fighting Game Eternal Fighter Zero, she's the only character who has two versions: An awake version who fights exclusively with kicks (Her upbeat and athletic part), and a sleepy form who fights with a parodied version of Drunken Boxing (Her sad part, except that she's asleep, and uses strawberry jam instead of alcohol to increase her offense and mobility). She received two styles because they reflect each half of her personality.
Either that, or Nayuki is such a prodigious girl that she mastered two fighting styles instead of just one. And EFZ runs on the Rule of Fun, so it is unlikely that she's sad at all, like the other girls, she's probably having fun fighting.

The Cute Ghost Girl that Mai can summon in Eternal Fighter Zero is a surviving demon.
Just because... someone has to link Kanon with EFZ.
On a (barely) more serious note, Mai seemingly hunted all the demons, except for one, the strongest of them all, who understood the futility in trying to escape or oppose, so, it performed a Heel–Face Turn, and took the form of a little black-haired, bunny-eared girl, who appears in battle following Mai's command.

In addition to the WMG above, after reforming that last demon, Mai spread the remnants of her powers to other people, and the result is what we know today as Eternal Fighter Zero.
With the help of her ghost partner, Mai got rid of the positive remnants of her powers (Positive as there were no demons anymore), but unconciously she transferred them to other people, starting with her nearest friend Sayuri, who was blessed with Magical Girl powers and the ability to wield a Morph Weapon. After that, the powers were transferred to very close people to Mai, and they got powers and fighting skills according to her dreams and personalities (Nayuki fights exclusively with kicks because she's a great runner, Makoto is able to use explosives and a gun in battle, as a reference to her doing pranks, Shiori received ice powers to reflect that her illness became her best strength), calm and quiet Mishio Amano became a master with the spear, etc.
However, this also result in a Mass Empowering Event, as those remnants spread over other places of the Seasonverse, and we have, for example, Mio Kouduki and Misaki Kawana from One ~ To The Radiant Season; the former weaponizes several cosplay outfits, to reflect her fondness for theater, and the latter got wind powers, given how much she loves commenting on the wind; or Kano Kirishima from AIR, who always wanted magical powers, earned the ability to cast fire, ice and lightning spells. Those remnants were also able to trascend time and space, as they were probably able to revive Misuzu, and by consequence, bring Kanna to the present time, but that required a huge amount of energy, and that probably explains she's so powerful an SNK Boss. Why Yuuichi didn't receive any powers is up to anyone's guess, at least, Yukito appears as an Assist Character for Misuzu.
As retribution, the girls wished for the happiness of whoever or whatever granted them those powers, and Mai, who was powerless at that time, received back a good part of the power she spread, enabling her to fully take control of her ghost partner, and becoming a strong, calm and versatile Iaijutsu Practitioner, to go according with her personality and her brand new powers.
Or once again, EFZ runs on the Rule of Fun, and Mai is so calm and focused that she barely reflects any emotion, so it's fair that she can also have fun with the new powers and fighting style she received, specially now that there are no more demons to hunt.

And speaking of Eternal Fighter Zero, the girls were not exactly adapted to fight, they were already powerful and capable fighters to begin with.
Why not, considering that this story (As well as AIR and ONE) has to deal with supernatural events? Probably Ayu, Nayuki and the others were aware of the powers and fighting skills they received, but agreed to keep them in secret (Even from Yuuichi) to avoid causing damage to private property (Yeah, they're that powerful), to avoid being labeled as "freaks" or something like that, and because such skills are irrelevant to the events taking place anyway.
Further evidence is that the stages are empty, empty in the sense that there is no people watching the duels, cheering for their favorites, which makes sense as they probably fight in private to keep others from getting hurt in the crossfire. Ayu's tree, Monomi Hill, the school courtyard at night, even the Minase residence are good and safe places to have off-screen duels without worries.
Although there are certain things this can't explain, as such powers and fighting skills could have prevented the plot from even unfolding: Mai, for example, could have used her iaijtusu technique from the beginning, and called her ghostly younger self for help, to literally clean the school up of demons in a single night (Or, since her EFZ powers are different, there would be no demons in the first place), Ayu's and Makoto's powers would have allowed them to stay instead of disappearing provided they kept fighting (Hence the "Eternal" in the title), Akiko could have easily caught that car that ran over her and thrown it like she does in EFZ, and Nayuki... well... as stated above, she's such a prodigious girl: Captain of the school's track team, and master of not one, but two styles of close combat.
Or once again, EFZ runs on the Rule of Fun, they were put into a Fighting Game because it's funny (and heartwarming) to see a group of cute girls throwing down for no particular reason, and being happy. No need to "bring tissues" anymore.