The thing you absolutely have to keep in mind regarding FLCL's story is that it is a parody, above all else. With that in mind, Furi Kuri is the story of Naota Nandaba, a twelve year old boy that is not only prematurely, but well into the moody teen years of his life. You see, Naota has a single, major problem - his older brother, and that despite the fact he's off playing baseball in America, his shadow is plenty long enough to entirely envelop Naota. Just how bad is this? Even his friends usually call him by his brother's name, and his brothers ex-girlfriend, Samejima Mamimi, hangs over him as though she expects Noata to pull his brother out of his pocket at any second. At the very least she's intent on turning him into a replacement for him.
Top that off with the fact that his father is an absolute nutcase and his grandfather isn't much better, and you know you've got all the makings for interesting times. The cherry on this particular cake is that the town they live must have been imported from the Twilight Zone. Centerpiece of the city is a giant factory that looks remarkably like an iron - right down to the steam it blows off once a day, covering the entire town in thick fog that effectively cuts off the outside world. As Naota laments in the early lines, nothing amazing ever happens there... nothing out of the ordinary. Did I mention the town had to have been imported from the Twilight Zone, folks? Hopefully you get an idea of 'ordinary.'
Enter Haruko Haruhara, who introduces herself in a rather distinctive manner... she runs into Naota on her Vespa, gives him CPR that looks suspiciously more like a very protracted kiss in the hopes of bringing him back to life... and then promptly slams a motor-powered guitar into his forehead. This is all in the first ten minutes, folks, and the story never gets any more more coherent - at least, not on a superficial level. Again, you have to remember that FLCL is a parody, so if you watch only for the superficial level of the show, you're just not going to get it - and more than likely think that the characters are all on the really GOOD crack. The first episode alone parodies Evangelion, Ogenki Clinic, Gundam, and even a couple series that I didn't recognize off the top of my head.
With that having been said, the series actually does manage some decent drama on the top level, mixing it well with the parody strewn all throughout the plot. The episodes seem very disjointed at first glance - and second, and third, an effect only aided by the fact that the fourth wall is broken freely by the characters. But the real beauty of the series is that it's written in such a way that you almost always catch something new with each viewing, until everything comes together and you realize that everything is linked together in very subtle ways. There are about eight separate sub-plots that showup to varying degrees that help tie the storyline together, and plenty of funny bits and nods to other series.
Another of the things that keeps the OVA moving along smoothly is the music, which does as much to tell the story as the dialogue itself. The whole soundtrack was done by the J-Rock band The Pillows, and vocal songs are often brought up in place of more extended dialogue. Unlike most series, where music played like this can become overwhelming, FLCL manages to pull it off without the music growing irritating. That's as much because the series comes off like a six episode long music video as it is because it was very skillfully done. Fortunately, the soundtrack is good enough to pull that off, so.
The voice actor side of things are alright. While there aren't any stellar performances, the dialogue comes off well and the emotional lack that occasionally plagues anime series is blissfully missing from FLCL. Haruko's VA is arguably the best of the bunch, what with the vocal obstacle course she runs as the series plays out. Noata's isn't bad either, though he does occasionally drop into a bit of a monotone that admittedly fits the character.
Animation is actually one of the lower points of the series, though that's more because the artists were playing along with the parody themes that FLCL is built around. At various points throughout the series you see nods in the style of animation to everything from Flash - as in the media format - to Southpark. Unfortunately, while the switchover from one style to the next is seamless, it still breaks up the flow of the action as you go from one style to the next. I'll also admit that there's a certain... lack of detail to the animation when it's not mimicking another style. I'm almost certain that it's because the animation was CG and they forgot to clean it up properly.
Like I said earlier, you're going to think that the characters are all on the really GOOD stuff your first time through. There's nothing that can really prepare you for it - they're all absolutely insane. If you're not a fan of subtle humor, I doubt you're going to have a lot of interest in FLCL. Though there's a fair helping of sight gags and slapstick, the series strength is in the satire and parody that it contains. On the other hand, there's also some nice action scenes to be found, especially in episodes three and five that keep the series from getting too out there. Some people will probably balk at Naota's self-hatred, but I'd point out that I think I'd hate myself too, if I was as far under my brother's shadow as Naota is under his brother's shadow. It's worth checking out. If you don't wanna spend the money on it, CN plays it off and on during the late nights, so if you keep an eye on the schedule chances are good you'll be able to catch it.