This show's cute, horrific, terrifying, action-packed, funny (but only very sparingly), dramatic, tragic, unusual and artistic. The characters all take different Magical Girl character archetypes and deconstruct them, among other things. The action scenes are amazingly fantastic, and the animation is beautiful, with gorgeously-designed characters and mass amounts of Scenery Porn. The series has beautifully moving and unique music (what else do you expect from Yuki Kajiura?) that is utilized to its greatest effect in every single scene. Gen Urobuchi and Akiyuki Shinbo have created a magnificent tale blending Magical Girl, Horror, Drama, Fantasy and Speculative Fiction in the most poetic and moving way possible. Each episode gets progressively better and better than the last, and it won't let up for even a split-second. Each single plot twist is unique and unexpected, including, but not limited to Mami's death, the revelation of Puella Magi being first-form Witches, Sayaka's transformation into a Witch, Kyouko sacrificing herself to save Sayaka from a Fate Worse Than Death, and the entirety of episode 10. It is one of the greatest ever created, and Shaft's grandest work of all time.
All the characters feel like real people. Very few anime existing that achieve that.
The storytelling itself is amazing. There's so much foreshadowed and hinted at in the first episode alone that it makes re-watching after finishing the entire series almost a necessity. There are no plot holes, no cop outs, no loopholes, no convenient moments, no Plot Armor, no pointless fanservice, and no filler moments. The story is always on the move and it works entirely on things that are established early on or are revealed later. The character development for all the characters is fantastic and often heartbreaking. All of this culminates together to make every single episode get darker and more emotional as it goes on. By the end, you're in awe at just how big the stakes are and left wondering how they're going to solve this. Cue one of the most noble, heartwarming, and tragic anime endings of all time.