Puella Magi Madoka Magica
Good: This show has a reputation for being either brilliant or overrated, and as such I went in with extremely high expectations, so it seems wrong to say that the show wound up meeting them. But it kind of did, at least in its technical excellence. It is a really, really good series in many different ways. If you can adapt to the stylized, childishly simplistic art, the animation is gorgeous and beautifully composed. The music is terrific. The themes and concepts being addressed through the narrative are complex and weighty. The characters are easy to care about and reward you for doing so. The overall writing is excellent, and some of the dialogue is incredible.
Bad: I don't really consider this show to have much in the way of objective problems, aside from some potential issues with pacing and plot structure--the middle third of the show is kind of weak in coherent and substantial plot, and the function of the final two episodes as a satisfying resolution is questionable. Indeed a whole lot of the series relies on using emotion more than action to advance the story, which is always a gamble. If it works, it's fantastic, but if it doesn't, you've lost viewers. Which brings me to my point here. What I do consider the show to have is an enormous capacity to polarize its audience. Whether you like it or can't stand it is very strongly dependent on your preferences, so try to take that into account and by all means walk away if you decide it's not to your taste. But don't spoil yourself too badly investigating.
My Favorite Part: The tenth episode is, I think, one of the best individual episodes of anime I've ever seen. Madoka and Homura's relationship is completely heart-wrenching. Ultimately, though, the peculiarities of my experience with this series mean that right now my favorite part is probably the show's conceptual and thematic framework.
Comments: The problem here is that it took me nine episodes to shed the cloak of detachment I had made for myself out of spoilers and analytical thinking. I had the basic themes of the series mapped out by the fourth or fifth episode, along with how they corresponded to each character arc, relationship, and plot twist, which is really unusual for me and fiction. Since Madoka Magica relies heavily on emotional manipulation of the viewer, this was kind of a problem. I think I might be able to fix some of this through rewatching bits and pieces, but it's thrown the whole thing into a weird place for me. Even though it was ultimately Madoka and Homura who got through to me emotionally, it's Kyouko I'm thinking of roleplaying. And I have about ten years' worth of commentary and analysis to regurgitate. I don't know what to make of it all.
You should watch it if you...
♦ Have a fondness for the tenets of cosmic horror, but would like to see it brought down to a more personal level for once.
♦ Revel in angst and melodrama without shame.
♦ You'll notice I'm not rattling off anything about "strong female characters" or the like! It's true that this show pretty much exclusively revolves around teenage girls, all of whom are meaningful and active characters, but I think in this particular case, one's opinion of the themes and the atmosphere of the series outweighs that aspect too much for it to really matter. I should note that this isn't because it's a seinen show, though (and anyway interviews indicate that the creators weren't too wedded to the male demographic; they've said they targeted the show at adult anime fans in general), and in fact I'm pretty sick of being told that it's wrong to enjoy such stories when they're targeted at men or else you're a vile neckbeard. I will say, however, that there is virtually no sexual fanservice in this show, aside from some tame shots in the opening.
♦ Seriously, if you're of the Bujold school of thought that plots by thinking up worse and worse things to do to characters, this is up your alley. I don't know what else to say without spoiling more than I already have.
Notes on influences and other texts
If you like [X], you should watch this: Neon Genesis Evangelion, Final Fantasy VIII (or even what it could have been), Shin Megami Tensei properties in general and Persona in particular, Sandman (and a number of similar Vertigo properties, such as Lucifer and Hellblazer at its best).
Additional notes: There are also a number of other canons I can relate Madoka Magica to without making a clear proclamation that someone who liked them would like it--which is to say, they share philosophical influences, address some of the same tropes, grapple with similar themes, use the narrative for related purposes, but don't necessarily belong to quite the same traditions, and they definitely don't all reach the same conclusions. Roll call: Magic Knight Rayearth (there is a thesis to be written on the conceptual relationship between Puella Magi Madoka Magica and Magic Knight Rayearth), Princess Tutu, Persona (the second and third games the most, I think).