Donnie Darko/WMG

The Philosophy of Time Travel is a genuine prophecy containing precise instructions for Donnie.
You can find the book on several sites, copied from the now defunct donniedarko.com. It suggests that the majority of the movie takes place in a "Tangent universe" created by a paradox (the temporally misplaced jet engine), which is doomed to collapse and - unless measures are taken to fix the paradox - take the prime universe with it. Nature sensibly provides the tools to fix the paradox: The "living receiver", the person closest to the impact (Donnie), gains superhuman strength, guiding visions and some control over the elements, and people who see him react strongly to him because nature is telling them to help him in any way they can. Those who die in the tangent universe (Gretchen and Frank) are able to move freely in time and so tell the living receiver about his future.

It should be pointed out that, although this interpretation of the movie makes perfect sense and was published as Word of God, it's still only one possibility.

The entirety of the film, except for the very end, was a vision Donnie had of the future.
It is established that Donnie has visions of the future, be they vague worm-like distortions coming out of people's chests or cryptic hallucinations which (although he doesn't understand at first) tell him that one day he'll meet a guy in a bunny suit named Frank and shoot him in the eye. So maybe the entire film is one big psychic vision. Donnie sees this series of events unfolding, with his mother and sister and future girlfriend all dying and his own psychological disintegration culminating in manslaughter, and he sees one simple way of avoiding it all: he stays at home one night instead of going out and gets crushed by a time-travelling jet engine. A bit drastic, but hey, it gets the job done.

Incidentally, if this is how the movie is meant to be interpreted, then Donnie Darko has an epic vision of the future that includes him having other visions of the future. Recursive future vision!

There are people other than Donnie who remember the future-that-wasn't.
In the epilogue, Frank reaches for his right eye (the one Donnie shot) and looks shaken. Gretchen (poor girl, with that name) also seems a little more moved by seeing the accident scene than just "His poor family" (although maybe that's just overacting). Possibly, these people (perhaps specifically those people that died?) remember the events of the movie, even if only as a dream that they don't consider reality.
 * The scene of everyone involved waking up to the tune of Mad World implies that, even if no one else has memories of the future-that-wasn't, they've been emotionally affected in some way. It's something they can't quite describe, a fear or a sadness that nags them when they're reminded of the future-that-wasn't.

Donnie is Jesus in Purgatory.
It's obvious. There is more than one allusion to theology and the search for God in the movie. Also, both the story and the main character of the movie have some parallels to Martin Scorsese's movie The Last Temptation of Christ and how it characterizes Jesus; and this movie is one of the movies shown in the cinema where Donnie and Gretchen watch The Evil Dead.
 * Allow this troper to make a more elaborate guess along this vein. Donnie was a messianic figure who was supposed to die for humanity at a certain time. Due to the interference of Cunningham (who it turned out was a type of anti christ) Donnie became a Dark Messiah and began to destroy the world. However, in this reality Frank was still the only casualty to die directly by Donnie's hand and this resulted in some accidental transfer of Donnie's powers into Frank. Dead Frank saw that Donnie had to be stopped but he had already won in this reality so Dead Frank tore a jet engine from a plane and used it to carve a path backwards in time. Due to temporal strangeness Dead Frank arrived before the jet engine and called out Donnie because he intended to kill Donnie himself. Dead Frank discovered that he could not interact physically with people because his powers had been drained, and so could not kill Donnie, and the jet engine fell through Donnie's room at that moment. Dead Frank realized that the jet engine should've been the thing to kill Donnie but he could do nothing now. Dead Frank went through an unspecified number of loops and each time accidentally prevented Donnie from dying. Eventually Dead Frank realized that Donnie, like the Christ Figure he is, had to choose to die or his death would be meaningless. Frank then led Donnie through a series of specific actions that opened Donnie's eyes to what a terrible person he would become if he survived the jet engine. When Dead Frank ripped off the jet engine this time he gave Donnie the chance to go through instead of himself. Donnie accepted and wound up back at the very beginning. This time when Frank called out to Donnie to come out, Donnie ignored him and remained in bed, thus ending the destructive loop (but not exactly stabilizing it) and saving humanity from the destruction that he might have wrought. Everyone who was closely connected to Donnie in the alternated timeline retained some memory and feeling of what happened so they could serve as his "apostles."

The film is NOT about a stable time loop.
A time loop like that can't possibly be stable. If it was, then Donnie sends a jet engine back into the past that kills him. So if Donnie dies, then he can't live to the point in the future where he drops the jet engine -- which means that he didn't drop the jet engine because he wasn't there. But then the jet engine wouldn't have crashed onto the house because it wouldn't have been sent back by Donnie because he'd be dead. Thus, the time line would've gone differently, so the movie wouldn't have happened the way it did.

Therefore, someone else must have sent the jet engine to avoid this, and the change happens when he stays in bed rather than going sleep walking, rather than when he supposedly sends the jet engine back. A time loop where Donnie drops a jet engine on his past self would just make the universe explode with how confusing and illogical that would be.
 * The only problem I saw with that was that Donnie replaced his past self, which (unless he only switched places with his past self) shouldn't have worked if he was able to send the jet engine back to above his house instead of to some hangar (unless the engine just turned up missing from its plane, and it just wasn't shown). Donnie sent the engine back, then went back himself and split the timelines. In the second timeline, there was (presumably) a spare engine, since it was changed so that the engine was never sent back after the engine had arrived. It's sort of an ampersand shape, if you think about it.
 * It seemed pretty straight-forward to me. The 'tangent' was a cosmic fuck-up; a splintered time-line that wasn't supposed to happen. And the universe corrected itself, via Donnie.

Donnie switched places with his past self.
His past self knows nothing about what happened that month. His girlfriend isn't dead because he never had a girlfriend. He's got a bunch of cool new stuff. There's no pistol with his fingerprints on it that matches the bullet in Frank's head anywhere in existence. All he knows is that he has no idea what happened in the past few weeks, he doesn't have to take those stupid "no fear" classes with Farmer any more, and a girl with whom he had supposedly been associating for the past few weeks had been found seemingly murdered by his sister's friend in a bunny costume whose corpse was lying a few feet away.

It's a Dying Dream
Perhaps all of these events are running through Donnie's head in the last split second before the jet engine crushes him. He tries to imagine what would happen if he survived, and finds only oblivion and dead girlfriends. This is how he consoles himself in his last few seconds- for him, living would be almost as bad as dying.
 * Just chiming in here to say that I just re-watched the film and this was the exact interpretation I had of it. That Donnie realized he was about to be smushed arbitrarily by a jet engine and so, instead of a life-flashing-before-eyes sequence, he gets a vision of the future to try and justify his otherwise totally meaningless death. It kind of ties into the rest of the movie, too, which seems to be largely about not fighting fate even when you have the option to do so (particularly Donnie's conversation with the science teacher about following God's path or whatever). The only thing that doesn't make sense is why he would be laughing and giggling to himself before the jet engine came through the roof, but hey. Also, it seems totally incompatible with the Word of God, but that's why they invented Death of the Author, right?
 * The reason he would be laughing to himself in this case would probably be that he went mad from the revelation.
 * Honestly, I saw that as the actual plot. Makes more sense than any other thing about the movie.

Frank (the one shown through most of the movie, not the one at the very beginning, and at/after the party, and at the very end) was Hare.
Hare took Frank's image for a ride into the past to mess around with the local causality. Now Father Time's beard is all in a knot that can't be unravelled without breaking everything, which is all good fun for a Trickster. The shot-out eye is symbolic of it being a version of Hare where one of his stories involves him losing an eye.

Frank (the one shown through most of the movie, not the one at the very beginning, and at/after the party, and at the very end) was a re-invention of the Black Rabbit of Inlé.
To quote That other wiki: "The Black Rabbit of Inlé: Also called Inlé-rah, he appears in fictional rabbit folklore as a sinister phantom servant of the Great Frith; he is the rabbit equivalent of a grim reaper in human folklore and similarly ensures all rabbits die at their pre-destined time. He is the moon rabbit, and Inlé is the rabbit name for the moon." Frank manipulated Donnie throughout the film in order to break the time loop and ensure that he died when the plane engine fell into his room. The light shining through the eye wound is also reminiscent of moonlight and it helps that Frank is dressed as a rabbit similar in style to pictures of Inlé. Alternately, it's a take on Inlé as a unified being guiding those to their death under the correct circumstances and the film is showing the interaction of Death, fate and time together.

Donnie knows or suspects that Cunningham is a pedophile even before he sets fire to his house.
As we know, the coach of the dance team Samantha is part of pretty much worships Cunningham and refuses to believe that he can possibly be at all imperfect. So, if her idol wants private "coaching" sessions with dance team members, he could very easily arrange it (since the coach is totally blind to anything less than wonderful about him, she wouldn't be at all suspicious), meaning he might well have molested one or more team members. Either Samantha did in fact run into trouble with Cunningham and her big brother knows or suspects, or he's been around the guy enough to pick up on something creepy about him. This would explain the otherwise disproportionate level of hostility.

Cherita Chen became one of the scientists from the future.
The fading memories of the tangent universe left her with a fascination of time travel and quantum physics, due to her eavesdropping during Monnitoff and Donnie's conversation about the subject.

Gretchen Ross is not, and never was, real.
She was an auditory and visual hallucination invented by Donnie to cope with his alienation.


 * Gretchen can be seen after Donnie's death in the main universe waving to his mom and talking to his neighbour.
 * It's possible she was real, but the version of her that Donnie dated was a hallucination caused by him getting his hopes up too much after she sat next to him in class.
 * Gretchen only sat next to Donne in the Tangent Universe; in the real world, she and Donnie didn't know each other.

Donnie actually had a nervous breakdown and committed suicide.
Pretty much everything that happened in the movie was a "what if" fantasy/dying dream that he used to justify it in his mind. The subject of religion came up because he was afraid that he might go to Hell after he died, so he retconned his death into a freak accident as a way of comforting himself.

Several Mind Screws exist in one shared universe.
It all starts with HBO's Carnivale. Several thousand years ago, the first avatara appeared: one an avatar of good, the other of evil. Every generation, two new avatars were born. The avatars were receiving their good/bad powers from either the white or the black lodge. Had Carnivale not been cancelled, Word of God is that it would have ended with the Trinity nuclear test, in the mid 1940s. It's also stated that Sofie is the Omega: the last of the Avatar, neither good nor evil, the one who will bring about the end. So, in the mid 40s, the avatar lines cease. The lodges, however, continue to exist.

Without avatars to project their influence through, things start getting weird. Instead of only a couple of people with ties to the powers of good and evil, now the powers seem to "leak" out into the world. This brings us to Twin Peaks. The black lodge has Killer BOB, the white lodge has (perhaps) the giant. The two lodges try to influence people in the real world using dreams. Windom Earl, a truly evil soul, is being contacted by the black lodge. The hope to use him as their pseudo-avatar. Likewise, agent Cooper is being contacted by the white lodge, who need a truly good soul to defeat evil. The show was cancelled before this could be resolved, and the series ends with Cooper trapped (perhaps forever) in the black lodge.

As David Lynch has confirmed that Lost Highway takes place in the Twin Peaks universe, and since Mulholland Drive was originally meant to be a spinoff for Audrey, it can be assumed that these two movies play by the same rules. People are influenced by the two lodges, each trying to gain a foothold in reality without the use of a proper Avatar. As Mulholland Drive is revealed, this could be either the white lodge trying to make her face what she's done, or the black lodge trying to make her forget about it and join them. Similarly, many parts of Lost Highway can be explained as visions from the lodges, the Mystery Man being a creature similar to Killer BOB, etc.

It must be remembered that time moves differently in the lodges than on our plane of reality. In the Twin Peaks prequel movie, Laura is warned about events that won't happen until the series proper. With that in mind, let's take a look at events that happened in Middlesex, Virginia. The year is 1988, and Donnie Darko is a troubled teenager who frequently sleepwalks. He also has vivid dreams. One day, a vision of Frank the rabbit tells him to leave his room. Donnie does so, and his bed is then destroyed by a mysterious falling airplane turbine. Donnie is told that he has 28 days to prevent the world from being destroyed. Clearly, the white lodge is using Frank as it's voice to help Donnie save the world. In the director's cut, Donnie is often seen to "download" information, with close-ups of his eye and many numbers and images flashing by. The Word of God on this is that the information is coming from unseen beings from the future. In actual fact, this is the White Lodge giving Donnie info on future events which he needs to prevent. The story of Donnie Darko plays out over the course of about a month, before Donnie travels back in time and saves the world by letting the airplane turbine kill him instead of leaving his bed. The events that took place during most of the movie end up never happening. They were erased from existence. Of course, the two lodges still remember them, as they exist outside of normal time.

The earlier mentioned Lost Highway is likely a similar story to Donnie Darko, with one or more of the lodges creating increasingly disturbing alternate realities to try and aid their pseudo-avatar on earth. It's possible that. It's very probably that similar events happen very frequently. Perhaps it's one of the lodges itself that creates these alternate realities in a bid to save the world, or maybe it's the trapped agents Cooper and/or Jeffries trying to get someone to rescue them. Either way, these realities can't last too long, or the world eventually ends.

What happens if one of these alternate realities is not destroyed in a fairly timely manner? Southland Tales is what happens. It's not all that obvious in the feature proper, due to half of the story being told in a tie in graphic novel (whatever idiot thought that would work should be shot), but Southland Tales can best be described as the future of Donnie Darko's tangent universe. Since Donnie sacrificed himself and closed the tangent universe, our reality was saved. However, he did not destroy the alt. universe, instead simply closing it off. Since the tangent universe can no longer effect out own, neither lodge is influencing it. This means that the white lodge isn't acting to save this world, nor it the black lodge acting to destroy or rule it.

This universe begins to fall apart, starting with the discovery of the "fluid karma" that the Treer company finds while drilling of the coast of Israel. Fluid Karma is an organic compound the circles around the earth like a serpent. It can be assumed that our primary universe also has fluid karma, but it's only reachable through one of the lodges. It's likely that fluid karma is what flowed through the old avatars' blood streams (hence why their blood was blue). With no lodge to control the Southland Tales alternate universe, fluid karma leaks out into reality. Another side-effect is "Operation Dream Theory." Here's what the Southland Tales faq page on imdb has to say about that:

"'Operation Dream Theory' was an experiment created by Treer. The Treer generators were slowing the rotation of Earth by .0000006 miles per hour, which caused strange effects around the world. One of these was a rift created in the fourth dimension -- the fourth dimension being time itself -- at Lake Meade, which was discovered when an airplane flew through it and had all its passengers left with amnesia (bar one - Krysta Now, who gained psychic abilities from it). Once it was discovered, they sent monkeys through it, which failed (Boxer claims that only a human soul could survive the trip). After much trial and error with monkies, Baron decided to send Boxer through it - chosen because of his political ties and his celebrity persona. When Boxer (and Roland) traveled through the rift, it created duplicate versions of both -- one set of duplicates traveled 69 minutes back in time, while the "originals" stayed in their original time. There are now two versions of each co-existing in the same universe -- two Boxer Santaros and two Roland Taverners. Boxer's original self was incinerated in a car bomb triggered by Serpentine, while the duplicate Boxer is still roaming. "

Reality itself is falling apart. It becomes up to the two Roland Taverners to save (or more likely, destroy and rebuild) their crumbling, neglected universe. The tattoos of various religions and beliefs that cover Boxer's body and are "fighting to see who will will" could be seen as meaning what faith the new universe will follow after the destruction of the current one. After all, the predominant force in the "real" reality has always been the two lodges, absent from this universe. The movies ends with the Jesus tattoo bleeding, Christianity is the victor, and the new reality will follow the rules of this faith.


 * YouTube link