Wow, that was painful. Please, anyone reading this, don't bother with this anime. Go pick up a translation of the novels or the manga. I've only read brief summaries of the novel, but those summaries were enough to let me know how good of a show this could have been, and just how far BONES had to go out of its way to make the No. 6 anime a complete trainwreck.
The first three episodes of the show were really interesting. Not fantastic, but enough to get me excited. There's a strong sense of mystery pervading the first episode: Why is this kid being pursued? What's that thing in the center of the city making a strange noise, one that causes those that hear it to listen in seeming awe and reverence? The second episode continues to add questions, while starting up the plot proper as prettyboy Nezumi helps hero Shion escape No. 6 before Shion can be taken to the Ministry of Love. Excuse me, I meant the Correctional Facility. The third episode gives us our look outside the city, so we can see a town built from freedom and poverty, distinct from the strict control of the supposed utopia beyond the walls. At the end of episode 3, Nezumi, who has stated his disgust at No. 6, promises to reveal to Shion why he hates Shion's former home, and why Shion should too.
And then episode 4 comes, and we get nothing. Then episode 5 comes, and we get nothing. Episode 6? Nope. Episode 7? Still nothing. The show spins its wheels for four episodes, and Nezumi and Shion's interactions in each episode can be summed up like this:
Nezumi: I hate No. 6! I want to destroy it!
Nezumi: I'll tell you later!
Shion: I love you, Nezumi.
Nezumi: I hate you because you love No. 6!
Shion: Why should I hate it?
Nezumi: I'll tell you later!
And so on. Eventually, something happens that causes them to actually decide to get off their asses and finally do something. This is episode 8. There are only 3 episodes left after this. They spend this episode seeing a guy who helped build the city, and getting answers from him. Why Nezumi didn't take Shion to him as soon as possible and keep the plot going is beyond me. We do learn some very important things this episode, though! Namely, the government of No. 6 is actually... evil! This was in no way obvious based on the previous seven episodes, and is a giant shock to everybody. We also learn about something called Elyurias, but what that actually is isn't explained yet.
The next bit will be a bit spoilerish. It shouldn't be too hard to guess the basics of what happens, but if you're really picky about avoiding spoilers you'll want to skip ahead, or stop reading and go do something that isn't watching this show.
The final three episodes end by showing a staggering display of incompetence by every single character and organization in the show (save for one, although that character is basically lucky). Nezumi and Shion infiltrate the Correctional Facility by the dumbest luck ever. Had things gone slightly not their way, they would have died instantly the second they entered the building. They wouldn't know where they should even be going in this place if it wasn't for a magic voice inside Shion's head. The guards of the supposedly secure facility are dispatched with ease by the two infiltrators. And then when Shion and Nezumi finally get to where they were going, the person they were trying to save has freed herself just fine thanks to the previously-mentioned magic voice. A resistance movement within No. 6 tries to do something, but they just kinda set off some bombs and talk to no one in particular. Random eco-magic destroys No. 6, everyone who survived is happy, or something. We don't learn much of anything, and just when we think we might we get a huge slap in the face for thinking that we should know what the hell we just watched.
Those of you who pay close attention to the plot may notice that nothing Shion and Nezumi do actually affects it. They don't destroy No. 6, they don't save the West District, they don't save the person they were supposed to save, they don't save the innocents in No. 6 from the danger they're in. (The last one in particular was what Shion really focused on trying to do, before the show forgot that he was supposed to do that.) Everything that the heroes try to accomplish is done for them, and had Shion and Nezumi not been in the show, the plot would have been exactly the same. (I suppose there's one thing Nezumi does to help take down No. 6 at the very end, but nothing in the anime canon is preventing the one person who actually did anything useful from doing that as well. There's a reason for it in the manga, but the anime contradicts that reason.)
Character development was just as teasing as the plot. Sure, the relationship between Shion and Nezumi was cute, and the world needs more romances that don't make a big deal about the gender of the participants, but it didn't go much of anywhere. We'd watch Shion and Nezumi say the same things, and maybe kiss a couple times. It goes over better than the plot, since at least you know what's going on between the two, but still, it could have progressed a lot faster and gone a lot deeper. (I'd bet Nezumi would not have any problems going really deep into Shion's... feelings.)
At least the art looked nice, and the music wasn't so weird as to be completely distracting. I think that I'll probably remember the music most fondly, not because it was particularly amazing, but just because it was really strange. Also, Safu is the best character and I wish she'd be in the show more. (Apparently she has an expanded role in the anime compared to the novels, and considering how little she's involved in the anime...) Unfortunately, that isn't nearly enough to make this worth anyone's time, not when you could be reading the novels. Or Brave New World. Or 1984. Or watching Steins;Gate. Or Lucky Star. Or Blue's Clues. (At least you got to know the answers to the mystery at the end of each episode.)
(Update: Someone informed me that No. 6 is considered to be a novel, not a light novel. I've changed that up above. I've seen conflicting information about this, though, but this change hopefully will still make sense. If it doesn't, just pretend I said 'book' each time I said 'novel'. If that still doesn't work for you, replace it with whatever you want.)