This is a rehash of sorts, but I have now re-watched FLCL twice in the last couple months, and it has gone from near favorite to definite favorite. I have an actual legitimate blog entry in the works, don't worry. But for now, here's an older writeup.
What strikes me about FLCL is that it is both the farthest anime from literature possible and one of the closest.
Some of the visuals, like when Naota is shot out of Canti as a white hot bullet, and uncurls and cools off into his human form, just can't be done anywhere outside of animation. Ditto with a lot of the crazy facial expressions and the like. Same with the auditory facets.
But on the flip-side, it is rife with foreshadowing, motiff, symbolism, and satire. Enough to make you think it started as a book in some crazy corner of the galaxy.
I actually think FLCL succeeds in being one of the most thought provoking works of all time, in the anime world; a zany, postmodern, superflat work that encourages a discussion of it's recurring symbolism and social criticism. It's almost too much, in some respects, with even little details like right-handed or left-handed coming into play (left-handers being controlled by the 'creative' right hemisphere on the brain, and right handers by the more analytical right hemisphere). Naota lacking a mother makes him search for a sort of hybrid mother/lover (have to slip in some song lyrics) from all the girls he meets. The "relationship" with him and his brother is excellent; not once do we ever truly see his brother, but we understand perfectly what Naota is going through in his seemingly conflicting idolization and frustration with his older siblings' successes. Because of all of this, Naota tries very hard to be an adult by the way he acts and even the food he eats culminating symbolically in the phallus shaped bump protruding from his forehead, growing bigger as the OVA carries on. Naota's thus liminal state is abused by the sexual advances of Mamimi, who is looking for sexual output in the absence of her boyfriend, Naota's older brother. Mamimi is referred to as a "native girl" and serves as a critique of traditional Japanese sexualization and culture, in contrast to Naota's liminal state encompassing both Japan, and an increasingly American influence by way of his brother. Notice the baseball bat he always carries around that serves as both a reminder of Naota's brother and American cultural imports.
Haruko is completely alien to the the "Japanese" flavor of the other characters, not just in looks (her eyes and hair), but in the Italian Vespa scooter and the imported bass she wields. Naota is now caught between the influence of Japan; Mamimi, and foreign culture (mostly American and other western values) in Haruko. Interestingly, Haruko's randomness and seemingly overreaching assertions of control is portrayed mostly positively by way of Naota, who becomes increasingly infatuated with her (i.e., American/western culture). Haruko's supervision of Naota can be seen as a metaphor for American led reconstruction in post World War II Japan.
Ninamori provides the catalyst for Naota's ultimate choice between American and western culture in Haruko, and (arguably) traditional Japanese aristocracy and classism by way of the positive portrayal of Ninamori's upper class standing.
There's a lot of other symbolism; notice that when Naota discusses his older brother, an airplane is always shown flying overhead, symbolizing his departure from Japan, and tying into the ever-present American ethos. Obviously, the vast sexual symbolism (Naota's horn, which isn't so subtle) are going to be hit and miss for people, but I think the creators of FLCL did a good job, mostly, of making these meaningful as opposed to simply trying to sell sex. While at times it seems to be too heavy-handed or too frequent, I think it largely contributes to the show positively. Same with the self-referential nature of some of the fourth-wall breaking moments, which most works of any medium flounder badly with when attempted.
The parody elements also tend to be hit-and-miss with people. I think the bullet time effects are ok in their exaggeration, although in a world now inundated with bullet time parodies and jokes, it loses some of it's appeal that it had a decade ago. The Revolutionary Girl Utena references/parodies (notice that the "weapons" in each show are pulled form someone's body) are interesting if ultimately fairly simplistic. I think the South Park moment is pretty funny, myself.
Yes, this is all wrapped around a, what I think to be, successful coming-of-age story; Naota being a mostly everyday kind of kid growing up in not so everyday circumstances, but still grappling with the same issues that many of us will grapple with. Perhaps, at times, FLCL is too crammed and kinetic to make sense of everything it's trying to say, but I still maintain that it is incredibly important and largely very successful 21st century anime work.