It's one of those landmark anime that shifts a genre. It's basically Neon Genesis Evangelion for magical girl shows, but with worse-written characters and an ending that makes sense.
However I'm not really a fan of Gen Urobuchi's writing.
Firstly, let's let the guy speak for himself. I'm about to quote wikipedia, but they took it from an interview Urobuchi did with Ultra Jump Egg. He told them "that he believed the overarching plot of a story was more important than the characters within it. He indicated that he would first determine the actions and the ultimate fate of a character before even assigning it a name, and contrasted this with other writing methods which first focused on developing the characters and then creating a storyline for them to follow."
Personally, I'd describe what I've seen of his storytelling as idea-led rather than character-led. (All I've seen of his so far is this show, Psycho-Pass and and an episode of Aldnoah.Zero, by the way. I'm no authority on his oeuvre as a whole.) What he does excellently is to explore a line of thought. Psycho-Pass is a fascinating discussion of the consequences of taking away our responsibility for our own morality. However his characters tend to be boring. This show has a big advantage over Psycho-Pass in that fourteen-year-old girls fighting for their lives are more sympathetic than a police state's enforcers, but even so they have a tendency to come across to me as the plot's puppets, not its drivers. Whole episodes can pass without any scenes that I regard as containing drama, i.e. a character making decisions as a result of their motivations.
Caveat: my reaction is clearly atypical. Lots of people love this show. It was massively popular, as indeed was Psycho-Pass.
Let's consider Sayaka Miki, though. Theoretically, she's quite an interesting character. There's plenty there to discuss and analyse. The biggest thing in her life is visiting that boy, Kamijo, in hospital all the time. She makes a big sacrifice for him, which could be interpreted metaphorically (NOT LITERALLY) as losing her virginity to him if one's pursuing a reading of this show being about female sexuality. (This reading can be extended to all the characters and mostly works quite well.) However Sayaka's feelings are more complicated than she thinks and she ends up SPOILER and SPOILER, with her most important relationships being with other girls. There's Madoka, of course, and their other classmate Hitomi. Above all there's her relationship with Kyoko, which is saying powerful things about both characters and ends up becoming SPOILER.
In practice, though, I never really felt I'd got to know the character. The Sayaka-Kamijo scenes are written quite flatly, telling us information and character points instead of showing them to us. (Kamijo really is a boring character and it's not just me saying that.) The scenes are also joyless and negative and clearly meant to be that way. Anyway, Sayaka eventually does a big thing to help Kamijo, but her story's unfolded in such a way that the dramatic option would have been for her to refuse the call.
After that, Sayaka felt to me, dramatically, like a collection of beliefs and ethical principles in search of a character. She's an idealist when she's with Kyoko. Why? Isn't it Madoka who's the idealist? What in Sayaka's earlier episodes suggested that she'd be like that? Then I didn't really believe in her reaction to a certain admittedly extreme revelation later. Why's she being like that? No one else is going that far, after all. I can understand the shock, but... um, spoilers. Nonetheless that's something that could easily have been set up in her earlier scenes with Kamijo, who after all had been crippled in an accident and raises not dissimilar questions just through being there in that hospital bed. There's a plot explanation in SPOILER, but to rely on that is to turn the character into a plot puppet instead of letting their actions grow from character.
None of this makes Sayaka a bad character. There's a lot to her relationship with Kyoko, while the Sayaka-Madoka relationship at the beginning also has something to it, especially when you include their classmate Hitomi. However to me it's liable to feel sketched.
It wouldn't even have been hard to join the dots and make Sayaka more dramatically satisfying. Nothing she does is unreasonable. One could easily provide psychological context for her viewpoint. A million options spring to mind. It's just that the show doesn't try. It just presents it as a fait accompli, a logical consequence of its exploration of its ideas. Personally I reckon that might be a result of Urobochi doing plot before character. Knowing from the beginning what he'd had planned for Sayaka to do, it might not have occurred to him that it could have used more justification dramatically.
Alternatively, consider the conversation between Madoka and her mum in ep.11. The scene's rubbish. Theoretically it's fantastic, mind you, and strong actors in live-action could have had us in floods of tears, but in the anime it doesn't work. Leaving aside the issue of Madoka having been a passive protagonist (since that's a key part of the plot), let's consider her mother. We know her quite well and she voiced an important line of intellectual exploration in ep.6 that changed the direction of the story, but she doesn't really exist dramatically. Of course a magical girl's mother is always likely to be a peripheral character, but even so here we have a scene of a mother letting her fourteen-year-old daughter go outside alone during what looks like an "evacuate the city" level natural disaster. How does Urobuchi try to justify this? Answer: not with drama, but with an earlier conversation in a bar about mothers' relationships with their children.
Then there's the humour. There isn't any. Not only are these characters never funny, but they don't even come across as capable of being funny. (There's an exception, the schoolteacher, but she's a cameo rather than a character.)
The show works. Obviously, clearly, it works. Lots of people have been able to engage with these characters and of course I've been picking out examples that demonstrate what I'm trying to say. The girls' situation is ghastly and it would be ridiculous to claim that this show's characters are all passive. However I think Urobuchi is relying to some extent on the audience doing some of his work for him. (For example, he also does that thing he'd do again in Psycho-Pass of having a chillingly emotionless character who's eventually revealed to have moving backstory. Until that point, we're presumably expected to engage with this character on trust.) He's clearly an important writer, if only in the impact he's had on the industry, but I think addressing this issue could make his work more complete and satisfying.
Mind you, there's also the unrelated issue of "why should I care?" There's that too. Everything is hopeless, the characters are doomed and they won't even listen to each other. If everything our heroines do is pointless (as the show seems to be saying), then you might start to feel that watching them is pointless too. The ending pulls that back, though, with some reconstruction after all the preceding deconstruction. Personally, I liked that. Others have been annoyed.
(Is it really deconstruction, though, or is it just darker? There's nothing particularly deconstructive about making the girls fight with guns, bombs, etc. rather than the usual magic wands. It just makes the tone grimmer, that's all.)
Then there's the, um, surprising thermodynamics, given the scale of the universe, but I quite like that. If borne in mind, that adds to the untrustworthiness and/or almost Lovecraftian alien viewpoint through which information is being filtered.
I should mention the lesbian subtext, which is probably inescapable in any show that's claiming to deconstruct the magical girl genre. At the beginning, it's overt enough to be noticed by other characters, with Hitomi jumping to mistaken conclusions. Of course the show's only explicitly romantic relationships are heterosexual, but those are bloodless and distant compared with the girl-girl relationships that build up. It's also noticeable that the show's magical girl transformations are clothed for most of the show and only become nude in the later episodes, when those relationships are at their most intense. (I'm not going near the title sequence and its naked embrace between two Madokas, if only because that might just have been Studio Shaft improvising without input from the writer or producers. Nonetheless, I think trying to analyse that might make your head explode.) This show thus has an unusually large fanbase among lesbian and bi/pansexual women, since those themes are being built into the story more seriously than the usual fan tease or fanservice.
I love the visuals. It's Studio Shaft, not going batshit throughout (although Madoka's home and school can look like a designer's wet dream) but instead saving it up for the witches' labyrinths. There, the animation adopts all kinds of extreme styles, often I think drawing on children's book illustrations. Silhouettes like puppet plays, collages like Terry Gilliam... it's fantastic. (The witches are all characterised, by the way, if you look at what's in the worlds their madness has created.)
The character designs are kind of bland, mind you, but that's clearly the point. It's a deliberate contrast of form and content, drawing the girls to be as cute and generic as is traditional for this children's genre. One of my favourite facts about this show, incidentally, is that the Australian children's channel ABC3 aired it in full, almost uncut. Presumably they saw the first episode and the cute character designs, then looked no further. The show's diverse fanbases thus include some small Australian girls.
Weird footnote: there's a sequel. I find it hard to imagine, but there is. There are three Madoka Magica films, the first two being just series compilations (eps. 1-8 and 9-12 respectively) and the third being original.
I'm sure this show would be richer on a rewatch. We'd see a certain character's scenes completely differently, of course, but there will also be easter eggs as subtle as Madoka choosing a ribbon in ep.1. Similarly that teacher's comedy rantings are, from a certain point of view, a precise description of our heroines' situation.
Personally, I think the last episode saves the show. Faith and optimism is so fundamental to the magical girl genre that I think unrelieved nihilism would be missing the point. In fairness, that duality had throughout been a central theme of this series, if not even the central theme. It's the conflict between hope and blackness. Besides, this darkness is so very, very dark that much of the show feels predictable, in general direction rather than specifics. I'm not sure that yet another tragedy would have added much.
A more fundamental problem, for me, though is the Urobuchi factor. (No, not his "Urobutcher" nickname.) Characters feel like vehicles for ideas. It's "tell, don't show". They are undeniably strong and richly explored ideas, though.