I just finished watching FLCL for the first time (yeah I know I'm late). Let me just say...holy crap. That was the craziest and most confusing anime I've ever seen in my entire life, and I loved every minute of it. It's so brilliantly untraditional that you can't help but appreciate just how crazy it is. You don't learn what much of the story is actually about until the very end of the anime, though it isn't much of a wait since the entire show is only 6 episodes long. To put it as simply as I can, the story follows a boy named Naota, who one day runs into (literally) a girl named Haruko. As soon as they meet, Haruko smashes her guitar into Naota's head. After that incident, strange stuff from human sized robots to giant mechanical hands start coming out of his head.
There's never a normal scene in FLCL; the characters are constantly flying around in an uber-slapstick fashion and scenes whip from here to there in the most nonsensical manner. This is why the story is so damn confusing; it doesn't really follow traditional story telling methods and just does whatever it wants during the episode's duration. What I particularly loved were the pop culture references (which I was nerd enough to understand), with references to South Park (yeah, I couldn't believe my eyes) and GUNDAM. Yeah, I loved the Gundam reference. There's an insane portion of the first episode where the anime suddenly turns into a manga, and scene whip from one panel to the other. During that portion, they make the reference. The un-animated manga pages are below.
Also rampant throughout FLCL are sexual jokes and puns, which might fly over a lot of people's heads if they aren't particularly dirty minded (or juvenile). The anime is basically a coming of age story for main character Naota, who happens to be only 12 years old. That is a bit young for so crude introductions to sexuality, but its all in the humor of the show. Besides all the fuss of story and comedy, the action scenes are quite impressive. The animation is top-notch, so the over-the-top fight sequences are incredibly epic. Accompanying the action is some great music from Japanese band The Pillows, who's music is played all throughout the anime. It really fits everything that goes on, and FLCL would not be the same without it.
You learn bits and parts of the story as you watch, and you won't even fully understand after watching it a couple times. Don't sit there and listen to me telling you what it is, you really just have to watch it for yourself. It would be crazy to think you haven't already seen it years ago (like me), so go right now. Its all on youtube.