Kanon/WMG

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 Amane) 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.

"That Jam" is Jarate
Yellow? Check. In a jar? Check. Adverse effects on anyone who comes in contact with it? Check.
 * No. Ew.

Kuichi 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.

Freddy Krueger was involved.
Freddy was responsible for Ayu dreams but Jason Voorhees killed him before he could do any thing.