I don't wish to address WHO is Pinkie Pie: she's a bubbly and endearing mare that we all love, that also happens to be infused with the Element of Laughter.

What I wish to address is the following: whatever we say, we cannot be blind enough to say that Pinkie Pie is an ordinary pony:
She can walk from A to C without traversing the distance in the middle.
She can sprout extra legs at the drop of a hat.
She's clairvoyant, knowing stuff as when people are about to break a promise.
She can step into mirrors. She can hang upside down.
She can pretty much summon appropriate books if someone needs an urgent answer.
She can appear out of places were she never entered.
Different instances of her across the universe know what the others know.
She can store stuff in her mane and in random spots, despite the stuff being much larger than the crevice used to hide it.
She can predict the future, after a fashion.

In discussion with our fellow member Lunatic Scientist, he half-jokingly asserted that she may be a tridimensional projection of a N-dimensional creature that actually remains in some other universe.

On the story "When they found us", Zephyrus Scary proposes that changelings have been living hidden among ponies for ages, but that a given changeling is composed of several bodies that take turns at being a pony 'they' created. Pinkie happens to have eleven changeling bodies.

On the story An Infinite Number of Pinkies, AugieDog proposes Pinkie Pie to be the second incarnation of a pan-universal force that happens to be tired of eternal living and eternal laughter. Literally, Pinkie is the Alpha and the Omega.

On the story "Seeing the Pattern", Aegis Shield centres around Pinkamena being a second personality of Pinkie, who uses the Pinkie Sense to save people.

On the story The Great Alicorn Hunt, Pinkie just happens to have the innate abilities to "see" and interact with, apparently, at least three more spacial dimensions than anybody else than Luna, who can barely work them.

On the story "Stardust", Arad says that Pinkie can read Twilight's mind across hundreds of lightyears, can teleport baked goods across hundreds of lightyears, and can know the secret preferences of the intended recipients without having ever interacted with them. And I found it scary to think that I thought that it all made perfect sense.

And on "Arrow 18 Mission Logs: Lone Ranger", Admiral Tigerclaw says that Pinkie can step into shadows and cupboards and step out somewhere else.

So what do you think, people?

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she's the writers attempt at a walking fourth-wall joke.
Unfortunately, they also made her annoying as hell.

3332119 She is a transdimensional god who hangs out as a pony because policing the multiverse gets boring after an eternity or six.

Or else, at the very, VERY least, she's a prime example of what happens when you give an earth-pony enough magical power to make Twilight blush.

3332119 Pinkie is the result of an earth pony having as much magic as Twilight. Earth pony magic creates a scalar field of magic that usually only interacts with certain things: rocks, animals, crop plants, etc. Pinkie's magic effects other sapient beings creating mass unified hallucinations and also with every other physical entity near her, granting something approximating clairvoyance. Were she more focused and stable she could have been a princess too.

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She is a lost member of the trans-dimensional race known as "Phoenixes".

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tho to be fair, she wasn't too bad in seasons 1 and 2. It's 3 and 4 where she started to get into retardedly annoying

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She's a cartoon character..... but if you want a more reasonible answer for a show about talking ponies, then my answer is that she has some form of magic and it shows when she over exaggerates.

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In Three Magics by Arkansaw Pinkerton, he proposed that all three tribes had their own magics--both in what they saw, and how their magic worked--and in that story, Pinkie was the earth-ponyest of the earth ponies, in complete harmony with the land and everything on it.

3332119 She is an ever-living pony who is the result of a magical accident 2000 years ago. Said magical accident gave her these powers in every universe she exists in. There. Problem solved.

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Who said I was joking?!

Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn!

As we all know now, everything in Equestria contains some kind of magic. Ever wonder why ponies can take such a rough beating before actually showing signs of injury? this "magic" is infused with their very DNA, which allows them to be more stronger, faster, and smarter. Take AJ, for example.
Have you ever tried to kick all the apples out of a tree? (Without breaking your legs) Not just one, or 10, but all of them? If you were able to not only kick a tree with that force, but knock down every single apple, you'd need retardedly thick bones, and a massive-ass body to throw that leg around. The reason she's so good at it is that she's got something in her bones which allows her to kick a helluvalot harder, without breaking all the leg bones on impact.
Pinkie pie, on the other hand, can't. Besides the Apple family, there aren't that many ponies (Excluding Apploosians) who can do this.
Do you remember the episode Super Speedy Cider Squeezy 6000?
Fluttershy didn't knock them down, she took them off instead. Albeit, you couldnt see her, and she was moving really fast, but still. It may be that Pegusai and Unicorns can't do what earth ponies can.
(Addition)This may even include pinkie's crazy-ass ability to shatter the fourth wall. Then again, she's just a more adorable Deadpool.

Now, about Pinkie pie? She's just inherently random. I don't think there will ever be a real explanation to why she can do what she can do.

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The story "First Contact" tears apart and explains certain things in the show, for example, Pinkie Pie.

She's a Looney Toon.
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She's an incarnation of Thalia, the Cosmic Force of Laughter (the ability to identify and make use of Paradox) and she is aware of all her selves in all parallel worlds, which is why Pony Pinkie and Humanoid Pinkie each knew what was known by the other. And she smells like candy.

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...and she is aware of all her selves in all parallel worlds...

At that, I would imagine her to be one single individual mind spread over the multiverse, rather than a community.

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Well, loosely -- each Pinkie is an indidvidual and she knows what the others know as a sort of dream or background information -- it doesn't have the immediacy of her personal experience. At the same time, the knowledge of any Pinkie influences all the Pinkies. Also, a lot of Pinkie's intelligence is consumed coordinating all this knowledge. Thus she is a strange combination of innocence and experience, childishness and wisdom, foolishness and frighteningly vast intellect. Her view of reality is at times very alien to that of other Ponies.

My theory ties in with the idea that Discord's not a draconequus but simply prefers to look like one. Pinkie's a being like Discord, but she prefers to look like an Earth pony.

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I've cast Pinkie in my story as an extremely powerful earth pony mage, very much the Twilight Sparkle of earth ponies. Most of her powers kind of group together into bending time/space in general; creating something out of nothing, stepping between unconnected points, ignoring physical laws. They're all very flashy, but Twilight happily turns fruit into a carriage in one episode, so nothings beyond the scope of magic in the Equestria setting. Pinkie's even consistent enough with her abilities that I could easily see all her crazy antics as just a very niche school.

Pinkie Pie is...

*digs through research and personal theories*

...somepony that has abilities both of Chaos and Earth Pony.

And her predicting senses are based on harmonical imbalances.

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...somepony that has abilities both of Chaos and Earth Pony.

I don't believe this one works right, though. Pinkie has proven able to unnerve Discord a couple times, which would mean that, whatever she's doing, she doesn't depend on Chaos.

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She's the precognitive, reality-warping daughter of Cloudy Quartz and the Paradise Entity, a magically-enhanced artificial intelligence that was the ruling spirit of the whole G3 world, the World That Was Lost. When the G3 world was destroyed by the Cosmics, the Paradise Entity fled across the multiverse to find a place where it could restore the World That Was Lost, and it needed a Herald of Paradise. Pinkie Pie, reborn from its vast memories, is the Herald of Paradise.

I've always guessed that when Discord ruled Equestria, he put a small amount of his magic into the Pie bloodline and had it randomly manifest every few generations.

It's always fun when character speculate about Pinkie. But it's not fun when some omniscient being in the story just definitely answers that question, leaving no mystery. That's why I was disappointed in "Sweetie Belle and the Tablet of Knowledge": not only it's just trying to explain her using some 'god-like' character as a mouthpiece, it's trying to explain her using anti-scientific Naïve Lamarckism Theory of Evolution. Rest of the story was using real science, that's why it was so disappointing to see something like that,