Eureka Seven/WMG

The entire anime is an allegory for smoking.
As partially explained in this comic, lifting is an allegory for smoking. Renton wanted to be cool and smoke like all the cool people he read in the magazines but no one in his town was really that into smoking. Eureka is a metaphor for peer pressure, as she is the one who leads Renton into Gekkostate. Gekkostate, in this interpretation, is a major tobacco company that produces pro-smoking propaganda in the form of ray=out. LF Os are cigarette filters and battles between them are symbolic for gang wars. As well, when Eureka falls ill and is covered in a layer of scub coral, she is actually diagnosed with lung cancer but goes into remission. When her coralian features begin to show towards the end of the series, it is the cancer making a reappearance.
 * As well, Dewey is representative of the government's anti-drug efforts, with Anemone and theEND being promoted as a legal high.
 * No. Just no. Don't ruin this series for me, PLEASE! Besides, (while I realize this probably isn't meant seriously) it's loaded with holes. For instance, when Eureka's Coralian features manifest to their full extent, Renton calls it "beautiful." Nobody, not even a smoker, thinks lung cancer is beautiful.
 * He was saying she was beautiful despite the chemotherapy. Duh.
 * Weirder interpretation immediately below...

The above WMG is true, but it's all taking place inside Renton's head.
Eureka is really a symbol for an I Wished You Were Dead. He thinks her transformation is beautiful because it was what he really wanted, but earlier he was overcome with guilt over his wish starting to come true.

It takes place after Neon Genesis Evangelion
And not just because all anime are somehow related to Eva.

After the events of End of Evangelion (using the interpretation that mostly everyone lived and Shinji and Asuka were just the only ones on the beach), the Coralian came into being. Mass-production-like Evas were used to fight it off, but failed miserably, becoming entombed. Humanity fled to the stars in a WALL-E-style escape, and then. Most of history was erased, with the exception that the Novak family kept very detailed records. Upon landing, the Vodarac took up a form of land-worship as opposed to... whatever the main religion of the settlers was.

It's an allegory for Vietnam.
Gekkostate are the hippies. Dewey and the federation are the U.S. Armed forces. the Coralians are the VC. Dewey's "Orange" superweapon is a reference to Agent Orange, a chemical Defoliant used in the war. Brings a whole new meaning to the phrase "Charlie don't surf."
 * While not an allegory, the number of references to American counterculture of the Vietnam War era do majorly intersect with the war, making for references. The Orange probably being a major one.
 * To further this theory, Agent Orange is a chemical defoliant in a series of them used in the Vietnam War. They were used to destroy the vegetation in Vietnam which both cut off the supply of food to the Viet Cong and decimated the landscape so that they couldn't hide in the trees and grass. The name of this group of dangerous chemicals? The Rainbow Herbicides. What's Renton and Eureka's most powerful attack? A giant rainbow of energy called the Seven Swell that destroys everything around it, including the plants, and turns it all into salt/dust/stone. Coincidence? I think not.

The Movie is a Fix Fic written by Renton.
In the movie, Renton is portrayed as being closer to Eureka from the beginning, and having more respect for his piloting skills. Simultaneously, the crew of Gekkostate are shown as being selfish and immature. The whole setting seems like revenge against them for their neglect of him.
 * The fan fic was written by Renton from the manga out of guilt for losing the girl he loved. Dominic had a fatherly-like roll in the movie because Renton looked up to Manga!Dominic and wanted to learn from him.

The reuse of series footage in the movie is intentional.
Considering how a major theme of the Eureka Seven movie is about "rebirth" and "creating your own story" (e.g. Anemone's subplot, the movie's ending theme being titled "Storywriter"), it can be argued that the movie itself is a Subversion of the standard Clip Show movie, inviting you to draw parallels with the series:
 * In series, the characters of Holland and Talho are shown as being mentally immature adults, while in the movie
 * The new characterisation of the Sages as . On that note, the most level-headed members of the Gekko State, Hap and Stoner,.
 * Dewey, the series Big Bad,, and Anemone and Dominic are upgraded.
 * Renton
 * The book with the Contemptible Cover, originally The Golden Bough (a study of comparative mythology and religion), is now presumably a copy of Anemone's memoirs titled "New World Story".

The two kids seen on the cover for the last dvd are Renton's and Eureka's

 * Which would make the end of the series Babies Ever After. The pic is here for reference.
 * side-note, Does anyone get reminded of 60s/70s depictions of space and the future when they look at this particular picture? Because I do...
 * Holy shit...that could actually be true. They share a lot of features. In fact, it could be a bit too obvious. My guess is it was intentional.
 * I'd hope it was intentional. I'm not sure if it's canon or not, but I'd guess it is - it is on the boxart, so it had to be at the very least approved by Studio BONES.