I finished FLCL! I have no idea what I saw!
I think anyone who has ever complained that anime is strange and doesn't make sense should watch FLCL. This show makes Neon Genesis Evangelion look like Bob The Builder.
Every weird show is weird in its own way. FLCL doesn't have any of the subtlety and sinister undertones of Serial Experiments Lain; all of FLCL's strangeness is hurled aggressively at the viewer, shouting and stomping and calling attention to itself. FLCL doesn't have the artistic meanderings of Paranoia Agent; it actually sticks to a rather small cast of characters and the show's tone is, um, consistently bizarre in each episode.
Let's get the mechanics out of the way before I dive into spoilers. There are only six episodes, so there's little excuse to not watch this. I watched the first episode subtitled, then heard that the English dub was actually good, and watched the dubbed version for the last five episodes. I slightly preferred the dub, which is pretty rare for me; Cowboy Bebop is the only other anime I can think of right off hand where that was the case.
And the genre? Oh, it's just your standard action comedy drama sports high-school romance spy anime, featuring giant flying fighting robots.
I'm completely inadequate to describe what goes on in this show. I mean, I can summarize the action without too much trouble. There's an attractive female alien who rides a Vespa and hits people on the head with her Rickenbacker bass guitar; the young teenage boy whose head she hits gets a bump, and that bump grows into a horn, and then giant robots burst out of the horn and start fighting the alien and/or each other. That's the first episode. Things get a bit weirder after that.
It's a very loud show, and a very kinetic show. "Lain" had almost no dialog at all, and what little there was was usually whispered or typed; the difficulty there was getting enough information to piece together what was happening. In FLCL, the characters regularly yell at each other, and one guy (with pretty impressive eyebrows) surfaces in the second half of the series, apparently with the main purpose of providing exposition. We have lots of information, but it just doesn't cohere together.
And then there's the subtext. Oh, man, the subtext. I've been peeking at the AV Club's reviews of these episodes; I'd watched the first two episodes late last year, and got caught back up so I could be more or less in sync with the TV Club's view-through of the series. I'm a bit embarrassed to admit it, but I'd missed out on a ton of the sexual innuendo and metaphor in the show. I say "embarrassed" because, after having seen the first two episodes and not thought about the symbolism, when I was watching the remaining episodes I realized that almost everything is symbolism. That isn't much of an exaggeration. Particularly in the baseball episode, seemingly every line of dialog and every image on the screen has a not-at-all-subtle reference in human anatomy.
I think part of the reason I missed all the undertones was because the overtones are so pronounced. Or, to put it another way, because so much of the show openly talks about sexual matters, it didn't really occur to me that it might NOT be openly talking about some sexual matters. The first episode includes an amazing showpiece of anime, where the boy's... father and grandfather, maybe (I'm still a bit unclear on how everyone is related) eat dinner with him and the alien. The screen shifts from anime into a manga format, and a hilarious, perverted, wildly kinetic series of panels track the discussion, which does as much as anything to explain to show's title. Fooling around... fooly cooly... FLCL... Anyways, when you've got THAT thrown right at your face, you aren't necessarily going to spend a ton of time thinking about the horn growing out of Naota's head.
The stuff about sexuality and puberty is big enough that I'm tempted to say that it's the main point of FLCL, but I won't say that it explains everything. There's a ton going on there, and the revelations of the last few episodes (N.O. Channels, the Pirate King, Medical Mechanical, etc.), seem to have their own mythologies that are orthogonal to the story of Naoto maturing (emotionally and physically).
END MINI SPOILERS
It looks like there are reams of ideas that have been written about FLCL, and I'll probably peruse some of them to see what the consensus is to answer the question, "What the heck was THAT?!" I've also really enjoyed the thoughtful reviews and discussion of the show at the AV Club; I mostly avoided the comments as I was watching the show, to avoid getting too spoiled for future episodes, but I'll likely dive back in when I have time and follow what looks to be a very spirited set of discussions.
I can't really rank anime shows, but I do have mental categories for them: "Must Watch," "Should Watch," "Can Watch," and "Don't Watch". FLCL floats somewhere between the first two buckets: it's so audacious and so amazing than it's well worth checking out, even though I suspect that many people won't care for it too much.