Haibane Renmei/WMG

The Haibane are the souls of young children who've committed suicide, and the city of Glie is in Purgatory.
The "cocoon dream" that each Haibane has (and from which they take their name) represents their time and manner of death. Their service in the city is atonement for the "sin" of ending their own life. If a Haibane cannot remember his or her cocoon dream, they become sin-bound, their wings turn black, and they are unable to leave on their "Day of Flight" (i.e., ascend to Heaven). They are then forced to serve in purgatory as the titular Haibane Renmei, guiding the future Haibanes to their ascension -- hence why the Renmei workers wear wooden wings (having lost their own), can not communicate with outsiders or each other (other than sign language) and have to live in solitude from the humans -- all punishments Rakka is told she will face if she can't break from being sin-bound.
 * In support to the fact about punishment, Rakka's job was to harvest light flakes for the Haibane Renmei, and the Renmei priest gave her that job because she touched the Wall without escape intent.
 * The Haibane originally didn't have to be children for this. They could merely be turned young once they arrive in the city.
 * It's clear that at least the older Haibane are all suicides and all dreamed of their method of death, and this is a Purgatory for them; that the Haibane Renmei are those who lost the wings is a pretty good guess, and makes a lot of sense though we still need direct evidence to support it. Just two problems: how did the younger Haibane die, given they didn't have naming dreams? And what's the theological status of the humans in the town?
 * When the head Renmei was describing the fate of failed Haibane to Rakka, we're treated to a nice shot of his fake, belled wings. It's not proof, but it's a strong implication.
 * Jossed. A Be has stated that only the sin-bound Haibane have committed suicide.
 * No. A Be has refused to answer many questions about the series because he wants viewers to come to their own conclusions. This is exactly the kind of thing he wouldn't say about it.
 * Those haibane who were born without sin are forced to stay in Glie anyway because, by living a humble, peaceful life without luxuries or vices, they have a chance to purify their souls from the sin of suicide before being accepted in Heaven.

The Haibane are just children who died before their time and have been given a chance to redeem their sins in purgatory due to their youth.
And the sin-bound Haibane are the only ones who committed suicide; they need to forgive themselves as well as serve their punishment before they can move on.

Haibane are not born sin-bound. Reki just got off to a bad start.
Haibane become sin-bound when they give in to despair and loneliness. Reki was born alone, trapped in a locked room. While trapped, her wings emerged, a very painful experience. Sounds like just the thing to give someone a cheerful and optimistic outlook on life, no?

Haibane Renmei is set in a Buddhist Cosmology.
A Haibane which attains their Day of Flight accends to a more enlightened world. Failed Haibane live out the rest of their days as Haibane Renmei, and maybe reincarnate as humans a few times before getting another shot at it.
 * There may be more than one road to enlightenment, the majority of souls do not become Haibane, and the Haibane Renmei are not guaranteed to return.
 * The Haibane Renmei may still reincarnate into a more enlightened world (the Renmei translator springs to mind), they just don't get a fancy lightshow.
 * Once a Haibane losses his wings and Halo, they are essentially human and can reproduce normally (Haibane are born from cocoons, remember). Consequently, there is now a colony of ordinary humans living in this waypoint for souls seeking enlightenment.

The Haibane never died in the first place.
They're people who, for one reason or another, retreated from society in the world and disappeared as a result. Hikikomori, like the eventual fate of Serial Experiments Lain and Welcome to The NHK, which Yoshitoshi ABe provided the scenario and design for in the former case and the original cover artwork int he latter. Their cocoon dreams are metaphors for the behavior the Haibane was in before disappearing -- Rakka rejected the help of someone trying to bring her back into society hurting the person in the process, Reki had many people who would have helped her get back into society that she never paid attention to and was unwilling to ask for help, Nemu slept her life away. Their time in Old Home is designed to force them into society: they must work with people, don't remember the part of the past that caused them to leave society in the first place. Sin-bound Renmei are just those who don't go into society fully with the other Renmei or townsfolk.
 * They did not only have problems with other people, but also with themselves. Kuu tried to be someone else by buying a bigger coat, by wearing Hikari's glasses and by driving Reki's scooter. When she accepted who she was or got comfortable with herself, mainly by being Rakka's mentor, she attained her Day of Flight.

Glie is actually a domed city, created by the Washi, the Proxy who reigns over it.
No one is able to leave the town except for the Toga because the Toga are able to survive the irradiated wasteland outside. The cocoons are hand-planted by the Washi as his own form of the incubation machines used in Romdo, and the Haibane are merely the children of the human populace; the dreams are a harmless side effect and truly mean nothing. The Day of Flight just strips the Haibane of their wings and halo, placing them as a normal human, as well as possibly their memories as a Haibane.

Reki's Dream is a continuation of her real life
Reki was in the process of committing suicide by getting her run over by a train, when she was removed from "our" world and transferred to Glie. In the last episode, she continued her dream in order to finish her suicide. She could not remember her dream because she was not sure if she wanted to commit suicide anymore.

Reki's Dream is a metaphor for the consequences of her emotional hardness
Reki closed herself off from everybody else, because even though she helped other people, she never let them help her or showed them her emotions. As said in the last episode, she wanted to become a stone, because a stone does not feel pain. This started before she got to Glie. By trying to shut down all emotions inside her, and by hating herself when she still had any emotions, she effectively killed herself: She got run over by her way of coping with the pain she suffered in her life before Glie.

Glie is a consensuous hallucination
The Haibane are people who retreat from others because they have been hurt. They fantasize about a town where they are accepted and life is not without hardships -- that would be too unrealistic -- but peaceful and friendly. When they have become strong enough to face reality again, they have their Day of Flight.

The Haibane are the souls of abused children who died in ways related to said abuse.
Only their memories of their previous existences are lost, so they don't remember being abused, and are given a comfortable life in the town of Glie. It was mentioned elsewhere in this article that "A Be has stated that only the sin-bound Haibane have committed suicide"; assuming this theory, this would probably mean that the sin-bound Haibane killed themselves in order to escape.

The Renmei's sign language...
...was originally the Daft Hands routine. Over time, they learned the words off by heart and no longer needed to play the music or write on their fingers, since they could all remember what it meant anyway. Over many generations, the routine mutated into a full blown language.

Reki is Paula.
Which means she's just a selfish little jerk who ended up throwing herself in front of a train. Not an interpretation of Reki that I'd like, but whatevs.

Also, they both have black hair and smoke.

Rakka was Lain
Lain was a lonely, reclusive, insecure and confused girl who thought nobody would notice her disappearance -- except for Alice, who was her only friend and stayed with her until the very last moment, even when finally confronting Masami Eiri. Despite this, she deleted herself from existence anyway, and very possibly offed herself afterwards. Having offed herself with the sin of hurting Alice, she was reborn as a haibane -- as the insecure and confused Rakka, that is, and Alice was the bird who tried to stop Rakka's fall. Rakka making amends with the bird, thus, was Lain making amends with Alice.

Evidence supporting this claim is the fact that Rakka looks like Lain with wings and longer and loose hair, and the fact that Yoshitoshi ABe was behind both productions. On the other hand, though, the omake found in the artbook has one of the two cocoons that appear at the end of the series turn out to be Lain.

Alternatively, Rakka was Sheeta from Miyazaki's Laputa: Castle in the Sky.
As well as Sheeta's apparent affinity for falling, the two are similar physically (especially at the end of Laputa: Castle in the Sky, when Sheeta's hair is randomly shortened) and in personality. The crow in Rakka's dream and at the bottom of the well is actually Pazu. Furthermore, the glowing flecks that Rakka is harvesting inside the wall of Glie look like they could contain or be made of Volucite, a further implication that the stories' universes are connected.

The Haibane are clones.
The story is similar to the movie the Island. The Haibane are clones of people living on the outside, and their entire life is centered around work that is designed to keep them healthy for whenever a client needs to harvest their organs. The wings and halo probably work as biological monitors, like the tags on wild birds, that can track runaway Haibane and send out to cloning lab scientists how healthy the clones are for organ donation. That explains why there don't seem to be any elderly Haibane and why the lives of the Haibane are tightly restricted. The priests are actually people in costumes, not supernatural beings, and they use metaphysical trickery like a fraudulent psychic or magician to keep the Haibane in obedience.

Glie is the same place as The End of The World
Albeit maybe before or after the events in the book.