Averted with Madoka's mother who is implied to be a big whig at some company.
Played with in regards to Kyubey's countless clients over the ages, which include Joan of Arc and Cleopatra. Kyubey claims that without his Miracle Contracts, humankind would still 'be naked in caves' which implies the wishes were helpful for these woman. However, Kyubey's gender is ambigious if the Incubators have genders at all. Second, considering how helpful Kyubey is after the contract is made, his clients still did everything themselves. Third, if Kyubey is right that humans would still be cavemen if he hadn't made contracts with certain girls and women, it implies that the male half of humanity did absolutely nothing.
In Episode 6, Madoka nearly kills Sayaka by throwing her soul gem away in order to prevent her from fighting Kyoku. She hoped that by throwing away the gem she could prevent one of them from dying.
Episode 10. The very first timeline was comparatively mild: Madoka and Mami defeat Walpurgisnacht and die in the process, without becoming witches. Homura wishes to redo it to save Madoka and with each attempt the endgames becomes worse and worse, down to Madoka becoming a super powerful witch and destroying the world. Episode 11 drills it in: Homura was giving Madoka more power with each reset by creating alternate universes. Greater Magical Girl translates into greater Witch power. In Episode 12, Madoka has enough power to bring the whole universe to an end. However, Madoka turns this around into an inversion. Homura's time loops gave Madoka enough power to break the system and achieve a better conclusion than the original timeline.
Kyubey grants Homura's wish to redo her meeting with Madoka and protect her instead of being the protectee. This means granting her time travel magic that can be used to learn his secrets and warn other magical girls.
Kyubey sends an Exposition Beam / Mind Rape into Madoka (who is not a magical girl) in order to explain how much he's done to/for the human race. It's implied that this is inspiration behind her wish to retro-actively destroy every witch ever and thereby reshape the universe into one more in favor of magical girls.
No Body Left Behind: This can happen to a witch's victim if they get stuck in the witch's Pocket Dimension after the witch is destroyed. The final fate of all magical girls in the current timeline, including Sayaka, as Madoka takes them to Heaven, body and all, at the very moment they'd normally be slated to become witches.
No Conservation of Energy: Played with! Conservation of energy totally applies... to everything EXCEPT magical girls. Kyubey is acutely aware of this and is exploiting it in the fight against entropy.
No Sell: During Homura's fights with Walpurgisnacht in episode 11, she launches a massive attack against the witch, utilizing a variety of weapons such as rockets, mines, and missiles. It doesn't affect the witch, and Homura's attempts to stop or slow her down fail.
Not So Different: Episode 7 implies this between Sayaka and Kyoko; both of them made selfless wishes for the sake of a higher ideal and were eventually broken by their wish backfiring. The only difference is that Kyoko became jaded instead of a monster.
The Obi-Wan: In the final episode, Kyoko and Mami return in a dream-like sequence to discuss things with Madoka.
Official Cosplay Gear: There are official soul gem necklaces. However, they aren't cosplay gear as such — they're smaller than the canon Soul Gems — and are more intended as jewelry.
Official Couple: Hitomi confesses to Kyosuke and they are seen sitting and talking together later.
One reason Homura is so callous is that every time she has been a friend and hero, she's failed to save anyone. This time, she's trying a different tack, doing whatever it takes to prevent Madoka from becoming a magical girl, no matter how much she gets hurt in the process.
One Degree of Separation: The third drama CD reveals that Kyoko and Mami worked together before the events of the anime. This was subtly hinted at in the anime proper. Then it further reveals that Kyoko once helped Madoka and Sayaka escape from a witch. This was not hinted at the anime because Madoka and Sayaka never actually saw Kyoko.
By combing her Time Stands Still ability with a sufficient number of guns, Homura can make herself a literal version of this trope. Stop time, fire the guns from different angles, start time, and an army's worth of bullets stream toward a witch.
One-Winged Angel: Charlotte in Episode 3. Starts off as a shout-out of Pukka and becomes a supremely creepy Takashi Murakami-style thing that looks like what you'd get if you mated a clown with a Sandworm.
Our Witches Are Different: They are reality-warping Eldritch Abominations with specific powers that seem to be based on a combination of the location they were born at and whatever they were feeling at the time. They are "matured" magical girls whose soul gems became too corrupt.
Out-of-Clothes Experience: Madoka and Homura in Episode 12 because they're somewhere between the physical plane and a higher plane.
Parental Abandonment: Averted with Madoka who has a nice happy family, but played straight with every other magical girl.
Mami's and Kyoko's are dead. The former by mundane causes and the latter's was killed as a side-effect of the wish.
Homura appears to live alone; the nameplate of her residence only has her name, much like Mami's. She is also conspicuously by herself when seen in the hospital, and seems to be the one filling out the forms to transfer to another school. The implication is that she's Conveniently an Orphan.
Sayaka presumably has them, but the only mention they get is when we hear Madoka talking to one on the phone in Episode 8. Her mother appears in Episode 11, during her funeral.
Plot-Based Voice Cancellation: Homura yells some things to Madoka in the prologue scene in Episode 1, but we don't hear it - and neither does Madoka. We learn in Episode 10 that she was begging her not to make the contract again.
Powered by a Forsaken Child: Kyubey's race decided they wanted to violate entropy and save the universe from heat death. The only way to do this was to find a source of energy that was not bound by the laws of thermodynamics. They settled on emotions and the greatest arc between hope and despair is in teenage human girls.
Homura: I'll do it over no matter how many times it takes. I'll relive it over and over again. I will find the way out. The one path that will save you from this destiny of despair. Madoka, my one and my only friend. I don't care. Because if it's for you, I'll stay trapped in this endless maze... forever.
Inverted in Episode 3. When Mami gets hyped up on the Power of Friendship during the battle with Charlotte, it leads to her fighting recklessly against the witch, as opposed to the cool, careful and methodical style of witch-killing she employed in the second episode, resulting in her freezing up when Charlotte goes One-Winged Angel, leading directly to her Cruel and Unusual Death.
The Presents Were Never from Santa: Sayaka (and Mami) falsely believe that their Magical Girl powers are righteous in nature, and people like Homura and Kyoko are misusing their powers for selfish interests. They are wrong, their powers have nothing to do with morality.
In Episode 10, Homura gives a tearful one to Madoka, promising that she'll stop her from making a contract.
Homura: I swear I'll save you! I'll do whatever it takes to keep you safe! I'll come back again and again and again! I'll save you, I swear!
In Episode 12, Madoka promises Homura that she will see her again someday. It's insinuated that all magical girls will be with Madoka after they run out of magic; she is shown collecting their grief and taking their soul gems.
Pyrrhic Victory: Any timeline where Walpurgisnacht is beaten ends up with Mitakihara in ruins and the combatants either dead or having used so much magic that they'll shortly become witches themselves.
First time - She fires a single arrow into the sky which instantly blows away the black storm clouds caused by Walpurgisnacht and reveals a brilliant blue sky. The arrow then bursts into an infinite number of arrows that shoot off in all directions. These arrows transcend space and time to save every single magical girl, past, present and future, from their Fate Worse than Death.
Second time - A galaxy-sized Madoka in what can only be described as her goddess form fires thousands of arrows at a planet-sized witch — the witch form of herself from the timeline that made the wish to save everyone, everywhere — that is threatening to end the universe. Everything is blown away.
Rapunzel Hair: Ultimate Madoka has the longest hair in the series as part of her goddess elegance. A design note advises that except for the ponytails on either side of her head, the viewer should never see the ends of her hair.
Read The Fine Print: Kyubey's contract has several unknown clauses such as: no wish warrantee, lichification, and inevitable witchifiation. He doesn't let them know there's a fine print in the first place but that's because You Didn't Ask.
Real Life Writes the Plot: The conversation between the two misogynists on the train in Episode 8 was based on a conversation Urobuchi overheard while riding on a train.
Reconstruction: Effectively, the Cosmic Retcon Madoka unleashes in the Bittersweet Endingrewrites the rules into those of a more traditional Magical Girl 'verse. Monsters still exist in the form of wraiths and magical girls exist to fight them, but in the recreated universe they no longer turn into witches, which no longer exist (not even Kyubey remembers them, and he scoffs at Homura when she suggests that they used to exist). Kyubey becomes a Deadpan Snarker assistant to Homura, while Madoka has Ascended to a Higher Plane of Existence as the patron goddess of magical girls. On the other hand, the reason magical girls don't become witches is because Madoka's ascension to godhood involved becoming the abstract concept of 'hope for magical girls' and causes their witches to vanish instead, while Kyubey's motivations and methods are unchanged... creating a world that's still realistic but not entirely back to the tropes that the show picked apart.
Madoka and Sayaka are at first hesitant to make a contract with Kyubey, which is only worsened after they witness Mami's death. Sayaka doesn't become a magical girl until Episode 4, and Madoka is a plain muggleuntil the final episode (which doesn't last long anyway).
Regular Caller: In the form of Kyubey, who tries to get Sayaka and Madoka to make wishes every episode and in the most pushy and manipulative manner possible. He succeeds with Sayaka after waiting until the exact moment that her friend hit the Despair Event Horizon, to say nothing about what he did to get Mami to sign up. He finally succeeds in the latter in Episode 12, but he was too clever by half. By explaining to Madoka the true story of the history of magical girls, he inspires her to perform a Cosmic Retcon ... and she's powerful enough to force him to grant the wish, much to his surprise — this is notably the only time in the entire series that Kyubey expresses any emotion on more than a superficial level.
Retconjuration/Ret Gone: Madoka's wish causes Witches to cease to exist because she causes magical girls to vanish before becoming witches. This makes her Ascend to a Higher Plane of Existence and erase every trace of her existence, except Homura's memories. It's insinuated that magical girls at the end of their lives also see her, and she can interact with them as a guardian angel.
The Right of a Superior Species: Kyubey plays with this trope. He turned vunerable teenage girls into magical girls in order to fight witches, but doesn't tell them that he does so by turning them into Liches. Then the girls find out that if they don't keep their soul gem pure, they become witches too, and it then it turns out he's doing all this to collect energy to fight the heat death of the universe. He justifies it by wanting to prevent said heat death, and by the fact that his kind has been assisting humanity since the stone age. All this while subtly implying that his race regards humanity the way humanity regards cattle. However, Kyubey doesn't have emotions, so he doesn't do this because he is thinks he superior to humanity (or at least that's not the most important reason). He does it because they need to prevent the universe ending, and this is the most efficient way to do it.
In regards to the series as a whole: Some people have called Puella Magi Madoka Magica the Anti-Evangelion, as the philosophy is entirely different. Whereas in Evangelion, the main character transforms from a depressed boy who hates himself to a happy boy who appreciates his shitty life in the last episode, while preventing the Assimilation Plot, Madoka transforms from a girl who hates herself to…a happy girl who essentially kills herself and disembodies her spirit in order to create a new system where all magical girls are saved while the Energy system is not compromised. Madoka let the Kyubey exist to prevent entropy and give humanity civilization, only now the worst and unnecessary waste products of the Puella Magi system (witches) are gone.
Rule of Symbolism: Everything references Faust; everything. Thanks to the Gretchen symbolism with Madoka and Homura's desire to protect her, Homura may represent Faust. Since different interpretations of Faust include both redemption and doom, one could argue both Homura and Sayaka are Faust.
Sailor Earth: Very common in fanfic; easiest is creating new magical girls; but also Kyubey variants with personalities named "Prefix"-bey are often villains or characters since Kyubey's personality is really tricky to do correctly.
Sanity Slippage: Poor, poor Sayaka...She losses sanity points by the episode until she finally becomes a witch.
Say My Name: In Episode 8. Sayakaaaaaa! This is notable for the fact that Homura showed a Not So Stoic moment and that Kyoko never calls anyone by name, then proceeds to spend a good deal of Episode 9 calling for Sayaka.
Schoolgirl Lesbians: Invoked by Hitomi who is convinced that Madoka and Sayaka have the hots for each other. In her defense, Sayaka spent the first episode giving her that impression. It turns out that Hitomi was aiming for the same boy Sayaka was aiming for, which gave her a reason to hope that Sayaka was a lesbian or at least lesbian-leaning bi or that she just preferred Madoka over Kyosuke, so they wouldn't have to "fight" for him.
School Uniforms are the New Black: The Mitakihara Junior High girls are rarely ever seen in something other than their uniforms and magical girl outfits. This averted in the manga, where Sayaka is shown in 'casual' outfits on several occasions.
Science Fantasy: Kyubey reveals that he and the other Incubators are an alien race trying prevent (or stave off) the heat death of the universe. However, he also states explicitly that magical girls/witches really are magic and this is why the energy they produce is effective against entropy; it's not bound by the rules of science.
Screening The Call: Homura is actively trying to prevent Madoka from becoming a magical girl. This is because the Madoka of a previous time line made her promise to save her from Kyubbey's trickery.
Screw Destiny: Homura's primary goal is to save Madoka from dying horribly or becoming a witch, as it happened many times before in many different timelines.
Senseless Sacrifice: From Kyubey's point of view, Kyoko's death was not this at all. It served a very important function for his plans. Due to her death, Homura must fight Walpurgisnacht by herself and both of them know she will fail. Thus, Madoka will be forced to make a contract to save Homura and the town from Walpurgisnacht.
Set Right What Once Went Wrong: The nature of Homura's powers and goal, as of Episode 8. (Later expanded on, in Episode 10.) Over and over again, Homura repeats the month of the series to save Madoka from Kyubey and death.
Fans have gone deep and wide to discover every single symbolism in the show; from the Witches' back-stories, meaning of their name and its connection to said back-stories, astronomy connection of said names, philosophical and psychoanalysis of the characters, foreshadowings, deciphering the runes, thermodynamic, Homura's time travel mechanic, Mitakihara's architectures and their comparison to the real-life buildings, canon's evidences of those yuri undertones...
Shoot the Dog: In Episode 10, in one of the previous timelines, Madoka asks Homura to kill her to prevent her from turning into a witch. She does it.
Episode 12: Homura's wings is one to Good Omens Death.
Episode 12: Madoka gives Homura her hair ribbons. This has been used as symbolic bonding between magical girls in Magical Girl Lyrical Nanoha.
Another one in 12: Madoka's speech as she tells off Kyubey for trying to renege out of fulfilling her wish ends with three sentences that are almost word-for-word from Sadako Sasaki's Memorial Statue.
Madoka:That's the only thing I want. It's what I wish for. Now grant my wish, Incubator!
Episode 9: When Kyubey explains the purpose of magical girls and witches, along with his real role in it to Madoka, several chairs similar to those on which characters from Bokurano sit while piloting Zearth can be seen in her room. Even more of these chairs are added in certain locations throughout the series in the DVD version.
Episode 9: Aspects of Kyoko's fight with Oktavia are reminiscent of Revolutionary Girl Utena, mainly the red and blue silhouettes of Kyoko and Sayaka melting together. Kyoko kissing her soul gem in a prayer position before her suicide attack is a more subtle one.
Mami's association with guns and Italian plus the fact that she became a magical girl directly after becoming an orphan is reminiscent of the protagonists of Gunslinger Girl.
Episode 12: Ultimate Madoka, aka Godoka/Madokami has a rather interesting similarity to the Mugen silhouette albeit more powerful. The similarities between the two are made obvious in this fanart.
Episode 12 also gives one to Fantasia with Kyosuke's music piece being "Ave Maria" - which the "Walpurgisnacht" sequence in Fantasia segued into.
"Sayaka" can mean "bright" or "fresh". "Miki" could be written as "tree trunk" or as "sake offered to the gods". Trees are generally associated with witches in the series, especially Walpurgisnacht, and an offering to the gods is a sacrifice. So Sayaka Miki is a "fresh sacrifice" whose very name foreshadows her becoming a witch.
Mami's first name can mean "sincere" or "protector", which fits her role as the mentor figure who helps convince Sayaka that becoming a magical girl is a good thing.
The kanji for Homura's last name means "never give up".
As for Madoka Kaname, her surname means "pivot" or "vital point", while Madoka means "circle". Madoka is the pivotal point in the circle—the one that everything revolves around.
Silent Conversation: Happens a couple times throughout the series. Mami's first encounter with Kyubey is shown without dialog, and Sayaka's reaction tells us she can hear what Hitomi and Kyosuke are talking about, but it's never revealed to the audience.
Sir Not-Appearing-in-This-Trailer: Kyoko gets left out of a lot of early promo material and barely appears in the opening, likely to preserve the twist of her first appearance.
Skyward Scream: When Homura sees Madoka next to Kyubey in the very first scene of the series. It's either a Big "NO!" or a Say My Name moment. It turns out to be a Big "NO!", since Madoka accepting the contract will end with her death and cause Homura to repeat the timeline again.
Slasher Smile: Almost everyone except Madoka has one in the manga. Kyubey is no exception.
Slice of Life: The anime is most certainly not this, but the second Drama CD is. On the other hand, some dialogue between Homura and Sayaka suggest the CD is not canon.
Sliding Scale of Idealism Versus Cynicism: Pretty far on the cynical side; Kyoko gives a speech about how magical girls are best off when they live only for themselves and Sayaka, who takes the opposite viewpoint is broken by her false(?) selflessness and becomes a witch. The finale moves things a bit closer to the idealistic side. Madoka becomes a godddess and prevents any witches from ever existing or having existed... but now demons exist, and the magical girls still have to fight them. Things are now less horrible and magical girls are more inclined to work together but most characters are dealing with roughly the same problems as they were before.
Shown Their Work: In regards to Homura's weapons, which are not only real-life weapons but also are drawn properly to detail. They even made sure to give Homura's Beretta M9 exactly 15 shots, which is its capacity in real life.
The soul gem of a magical girl is exactly what it is called.
On a smaller note, the grief seed of the witch is exactly the same thing.
Soundtrack Dissonance: In Episode 9, we're treated to soft, relaxing violin music as the magical girls fight Sayaka's Witch form, Oktavia von Seckendorff. Justified as it's a Song Of Solace for Oktavia.
The movie loves doing this with the witch fights as the original music has been replaced for most of them.
Runes in the last episode spell the anime's title as Puella Magi Madoka Magika. (However, the original Latin adjective is indeed "Magica", so this isn't debated.)
Kyubey can be Kyubey, Kyuubey, Kyuubei, Kyubei, Kyuubee, or even Cubé. The fact this comes from "incubator" does not help.
Kyouko versus Kyoko.
Spin-Off Babies: The novel features a kindergarten-aged Madoka and Sayaka meeting for the first time.
Spoiler Opening: The cover art (as seen in the picture above), and the opening prominently feature Madoka as a magical girl. However, we don't see her as one until episode 10, as part of Homura's backstory, which makes sense as she was actively trying to dissuade Madoka from becoming one in the first place.
This is somewhat toyed with since this raises the audience's expectations that Madoka will be a magic girl for most of the show and so spend the entire time expecting her to be one and are then caught off guard when it only happens so late in the show.
Standard Female Grab Area: Kyoko tries this on Homura, and it works! It's later revealed that this is because Homura's abilities are based on time travel. She can't escape a grab by freezing time. The trope is then defied when the 'victim' drops a live stun grenade on the floor and easily escapes in the panic.
Fans have noticed that the 魔法少女 (mahō shōjo, "magical girl") kanji in the title are stylized enough to make 廃怯少女 (haikyō shōjo, "faltering girl") a valid interpretation.
More important and lampshaded later: A young witch is a girl who uses magic, a "magical girl". What magical girls grow into was always inevitable.
This gets even more interesting and treads into Meaningful Name territory when you consider "廃怯少女": so a 魔法少女 eventually evolves into a 魔女, a witch, right? Going by that logic, a 廃怯少女 would mature into a 廃女, a haijo, or roughly a "girl who abolishes". Right, then: consider the ending.
Sayaka's witch is named Oktavia von Seckendorff and fights by summoning giant wheels. The German poet Karl von Seckendorff wrote The Wheel of Fate.
One of the explosion sounds from Mami's final attack hitting Charlotte in Episode 3 is the same as the sound of a warship exploding in Freelancer.
Stylistic Suck: An interview with some of the production staff indicates that Madoka's notebook sketches of herself as a magical girl were intentionally drawn somewhat badly in order to seem authentic. (The same interview also indicates that the first pass at those sketches were too far in the "suck" direction.)
Suicide Pact: Episode/Chapter 4. A witch trances a large group of people to gather in a warehouse and gas themselves to death.