The page image is Fate Testarossa from Magical Girl Lyrical Nanoha. She spends the majority of the first season attempting to gather the Jewel Seeds before Nanoha, at the behest of her mother, Precia. Eventually, she ends up severely overexerting herself in an attempt to obtain all of the remaining Seeds at once, and is stopped by a concerned Nanoha. Fate ends up returning home empty-handed, and the camera follows her. It is at this point we learn that Fate is a clone of Precia's original daughter, Alicia, who has spent the past thirty years in medical stasis after a severe accident. Precia considers her a failed project, does not acknowledge her as a person, let alone as a daughter, and lashes her with a whip when she doesn't fulfill Precia's orders. The aforementioned scene rapidly converts most viewers from enjoying the somewhat humorous tone and subversiveness of the series to "PRECIA TESTAROSSA MUST DIE".
The trope is Older Than They Think, as proved by Karen from the Sally the Witch second series. Karen was cast away from the Magical Realm of Astoria as a little girl alongside her evil father, was poisoned with hate by said father until he died, returned with a big grudge against Sally herself, attempted to separate her from her human friends via her black magic, was less purely evil and much more EXTREMELY bitter and hurt over being alone for years, Sally defeated her with both her magic and The Power of Friendship, AND she ultimately had a Heel-Face Turn.
Another very early example is Hilda from Hols: Prince of the Sun. She's a mysterious young girl who bonds with main character Hols, but she turns out to be the sister of the Big Bad Grunwald, and as the story progresses she's more and more conflicted about her loyalties.
Hotaru Tomoe (Sailor Saturn) is subverted. At first, the Outer Soldiers treat her as a Dark Magical Girl because they believe her awakening as Sailor Saturn would bring about The End of the World as We Know It. This turns out to be somewhat true; though Saturn does have the power to initiate an apocalypse, she would never do so unless ordered to by her Queen; however, in the present day her reincarnation is possessed by The Dragon, whose goal is The End of the World as We Know It. The protagonists are understandably confused about Hotaru's motivations for much of the season.
Dark Nana (Jamanana) from Seven of Seven. She is Nana's dark side/true self, born from her despair over Yoichi and left unnoticed, jealous of all the fun the others had. She has proven to be much, much stronger than the other Nanas, able to hypnotize people easily, teleport, fly with ease, fire energy blasts, and be a badaxe. In the end, she just needed a hug.
Mikoto Minagi from Mai Hime is truly innocent, sweet, and loving toward everyone she knows — but becomes a holy terror in the defense/service of the brother whom she has been seeking through the entire series, and who turns out to be the biggest Big Bad in the entire show. True to the form of the trope, Mikoto's convinced to do a Heel-Face Turn via The Power of Love from Mai, and then she frees her brother from his inner darkness by smashing his pendant with her sword.
Also from Mai Hime is Nao Yuuki, who travels the path she took because her father was killed and her mother was seriously injured by robbers. Unlike Mikoto, she doesn't get converted over as easily. Making Nao even more tragic, she was beginning to really warm to the group before Natsuki was tricked into attacking her. It's hard not to feel sorry for her when she leaves, screaming revenge and clutching what's left of her right eye, once you realize it.
Nina (among others) from Mai-Otome. Tomoe is an aversion; she's simply pure evil.
In HeartCatch, Yuri Tsukikage/Cure Moonlight also has some traces of this despite being on the side of good. Though quiet, mature and intellectual, she harbours a deep sadness within her heart, unable to forgive herself for her past failures that got her Brought Down to Normal and killed her companion. Eventually, she heals... and then becomes Cure Moonlight again. Incidentally, Dark Pretty Cure from the same series actually doesn't get redeemed, and is in fact Killed Off for Real. Though in a heartbreaking manner.
Suigintou of Rozen Maiden is developed into this role in the sequels.
Miyu of the Vampire Princess Miyu TV series starts out as largely this archetype — a reserved, lonely girl whose only companions are her Team Pet, Shiina, and her battle partner, Larva. However, she's a very atypical case, as she's the main character, and begins to grow out of it due to discovering friends, rather than being lured out of it by the magical girl. Her rival, Reiha, is a more straight example.
Saint Tail's mother in the manga Kaitou Saint Tail was a Dark Magical Girl named "Saint Lucifer" long before Meimi was born. Convinced to Heel-Face Turn by Saint Tail's father, they settled down together. (In the anime, she was always good, though more morally grey than Meimi.)
Crona the Demon Sword User from Soul Eater. His/Her mother, Medusa the Witch, "trained" Crona by forcing Crona to beat his/her pet rabbit to death, and locked Crona in a closet until s/he agreed to do so. Then they ate the rabbit. S/he also has the Black Blood taint and the demonic sword, Ragnarok. Maka befriended her/him with warrior therapy and became his/her staunchest supporter after the Heel-Face Turn.
Naha Midori from Telepathy Shoujo Ran, who was Genre Savvy enough to do an immediate heel face turn. She then goes on to get practically adopted into Ran's family, and spends the rest of the series living the good life. Ohara Momoko is a dark magical girl who grows up without going through the face turn, and is miserable because of it.
Utau Hoshina from Shugo Chara! is an example played straight. Though whenever Ikuto stops by, she goes from a serious and brooding dark magical girl to lovelorn and cutesy. After both of her Charas leave her, she gets some Epiphany Therapy and turns to the side of good.
Gaara, from Naruto, is a Gender Flip; a lonely antagonistic foil for Naruto who becomes a good guy and a friend after his defeat in part 1. The fact that both of them are jinchuriki seals the deal.
If the flashbacks are to be believed, Hinata could have been this if not Naruto's influence on her. She has the father-issues and the loneliness and 'group pariah' status as Naruto.
Yue Ayase is an interesting case who teeters back and forth on the edge of averting this trope for most of the series. Most of her "dark" traits are most apparent near the beginning of the series when her primary character attributes (apart from being Nodoka's best friend) involved being a slightly chillyBrilliant but Lazyserial snarker. In fact, Yue barely averts what could have been a Start of Darkness when her feelings for Negi led to her thinking that she had betrayed Nodoka in a moment of weakness; rather than face her best friend, she chose to run away, and were it not for Nodoka's timely intervention, poor Yue could have sunken to the emotional depths required for DMGs. Regardless, she doesn't unlock her magical abilities until a fair way into the series: by that point, she's warmed up to the rest of the group, effectively ditching the most negative DMG traits she had around the same time she became a mage. At this point, it's hard to say for certain whether Yue is a recovering DMG or just an unusually cynical/snarky Magical Girl.
We also have "Poyo" from the Rainyday twins, who has touches of Dark Action Girl.
Homura Akemi is the in-house poster girl for this trope. From the first episode she is a cold and aloof antagonist contrasting the warm and friendly Madoka. In truth she was Good All Along and has been opposing Kyuubey who is arguably the Big Bad of the series) and doing everything for the sake of Madoka. She invoked this trope for the sake of not getting too close to, and thus hurting, Madoka.
Kyouko is an anatagonistic Magical Girl but her foil is Sayaka. On one hand we have the red Social Darwinist and on the other we have the blue Knight in Shining Armor. They fight over their conflicting philiosophies but evenutally Kyouko reaches out to Sayaka in friendship and becomes a more heroic magical girl because Sayaka reminded her of the idealism she lost.
Sayaka herself is a inversion. She goes from traditional Magical Girl and isolation/despair drives her into a monster because Kyouko convinced her it was better to be selfish and she already had severe problems before becoming a Magical Girl.
Morgan Le-Fay is the closest to a Dark Magical Girl in the Ah! My Goddess franchise. She appears in the Movie, as a beautiful fairy who works as the messenger of Big Bad and Belldandy's first love Celestin, who sends her to drive Keiichi and Belldandy apart so he can use this to make Belldandy his Apocalypse Maiden and then go Rage Against the Heavens. It's later explained that Morgan lost her lovee when they couldn't go through the Gate of Judgement as a test of their love, which emotionally broke her; when Keiichi and Belldandy manage to pass through it in the end, Margan's faith in love and the world is ultimately restored.
The first Cardcaptor Sakura movie gives us Mahoudoushi/The Enchantress. The contrast with her and Sakura, the Magical Girl, is revealed over the course of the movie. Mahoudoushi is a lonely Hot Witch who practised Black Magic, and she turned sour after her lover and mentor Clow sealed her away. After fighting the Magical Girl and losing, she has a Heel-Face Turn, and manages to finally pass on in peace.
Also the Big Bad from the second movie... The Nothing Card. All that she wants is to have her old friends alias the other Clow/Sakura Cards back to her side. She reacts with fright, tears and screams if it seems someone will seal her away for a second time, then unleashes her magic in terror. What can she do with said magic? She doesn't so much as flinch to erasing an entire town's populace in her frenzied search. It is only when she realises such actions mean the cards won't accept her that she begins to doubt her methods, and Sakura then fuses Nothing with The Nameless Card, creating The Hope card.
Also Gender Flipped with Yue, who is something of a Grumpy Bear and was completely unwilling to accept Sakura until she defeated him. He also has Parental Abandonment issues since his beloved creator died, leaving him, Kero and the cards alone for a few centuries until Sakura found them.
The very uncommon mix between Dark Action Girl and Dark Magical Girl happens in Tenkuu Senki Shurato. Nara-oh Renge comes off as the first in the beginning, what with her genuine and huge fighting skills and her no-nosense attitude... but as the story continues, we see that personality-wise Renge is much closer to this trope: she's not a bad person in herself, just a confused and emotionally-broken young girl who sincerely loves her Evil Mentor Indra and has inner pain about it. After being killed in battle and brought Back from the Dead, Renge makes a Heel-Face Turn and is firmly on the side of good from then on.
Yugi from Tenchi in Tokyo, in a rare Big Bad example. She was an Artificial Human created for experiments and had few idea of how the world worked as well as how much she hurt others with her powers. This lead to ber being sealed away by the then-Juraian Empress (an ancestor of Ayeka and Sasami) as the only solution despite how she was terrified of darkness and isolation. She grew VERY bitter and brewed an Evil Plan to conquer the Universe (which involved creating Sakuya to break havoc among Tenchi and his Unwanted Harem among other things), befriended Sasami who became her Morality Pet (to the point of deliberately keeping her outta her plans, and then kidnapping her to keep her by her side). To defeat her Tenchi had to reason with her and pull her outta a Villainous Breakdown (in which she cries and screams that she doesn't want to be buried again) instead of killing her. One Cool Down Hug and she's redeemed.
Prétear's anime version of Takako/Fenrir is a rare Big Bad version. She broke down and had a Face-Heel Turn after having her feelings for Hayate rejected, which did NOT mix well with her deep insecurities. Like most Dark Magical Girls, she is ultimately redeemed and the last shot we see of her is her Happily Ever After with Sasame, her Second Love.
In the anime, Himeno's stepsister Mawata briefly plays the role after Takako uses her Heroic BSOD upon being cruelly rejected by a Face Heel Turned Sasame and being overwhelmed by her loneliness, then steals her soul and locks her in a magical tree. Himeno has to make a MASSIVE effort to get Mawata back, and then she goes off to face and redeem Takako.
Hiromi "Potamus" Kawanami from Wedding Peach makes a nice contrast to The Heroine Momoko. She's a devil Yandere and her rival in love. In one scene she transforms between human and devil forms by shouting her true name, similar to Momoko. Then she has a Heel-Face Turn.
Sorceress Arachnia in Tales of the Five Hundred Kingdoms is a lonely girl whose story was supposed to be something like Hansel and Gretel. Eventually she found love and decided she would be happier being good while appearing dark and spooky.
Regina from Once Upon a Time can be read like this - although she's of course not a "young girl" anymore. She's definitely suffered from an abusive mother and ineffectual and later dead (by her own hand) father. And with what she sees as Snow's betrayal, she lost both this blossoming friendship and her One True Love. Many of her major interactions after that - at least those not focused on revenge - can be read as her clinging too tightly to everyone who could prevent her from being alone. And it even looks like she might eventually be redeemed by befriending The Chosen One.
Mokou is an odd example in that she has all the earmarks of this trope, but her image is overshadowed by her on-off rivalry with Kaguya and her interaction with Keine. And she wears suspenders and red poofy pants.
Chidori Yoshino from Persona 3. She has inborn healing powers, is a Persona user who survived hideous experiments, needs drugs to survive ( more exactly, to keep her Persona from killing her)... and she's also a part of Strega, a group that opposes the protagonists. For worse, she gets in a Star-Crossed Lovers deal with The Lancer Junpei, and pulls a Heroic Sacrifice for him. You can give her a happier ending in FES, but it's not exactly easy to achieve.
Jacqli in Ar Tonelico 2. She begins as a non-quite-antagonist who eventually joins the main party after a number of battles. She's cynical in contrast to the heroine duo's idealism and wears wears dark clothing to contrast their bright colors.
Bloody Marie of Skull Girls who is not evil herself but was changed into to the titular monster because she used the Skullheart to wish vengeance upon the Medici mafia. Peacock, despite her extremely twisted nature, is the good magical girl counterpart.
MegaTokyo's Tohya Miho: we've seen her flip a van with one hand, jump three or four blocks whilst carrying Kimiko, and walk nonchalantly on telegraph wires, and the held-back tears give it away when Kimiko tells her that the lack of emotional connection to others necessarily means the lack of what it is to be alive.
In the Mechagical Girl Lisa ANT, the character Pink Flash is a inversion: she is a mercenary who willfully works for evil alien invaders (as opposed to Lisa, who works for other evil alien invaders because she's too gullible), but she is anything but dark.
Angel Moxie, itself a pastiche of Magical Girl and Anime tropes, had the character of Tristan fill in the role of the Dark Magical Girl. She worked for the villain near the start, but she quickly changed sides after being betrayed.
In To Prevent World Peace, the main character (a villain) takes down dark magical girls in order to make the nice ones stronger.
Tami from the web novel Dimension Heroes is brainwashed into working for the evil Dark Lady Scortana, resulting in a radical change both in personality and wardrobe.
Teen Titans features both Raven and Terra, both Tykebombs, each with their own Dark and Troubled Past who are ultimately unwilling servants of their abusive parental figures, struggling with their transitions from Face to Heel and back again.
W.I.T.C.H. features an interesting variation. The Dark Magical Girl Elyon Brown, alias Princess Elyon from Meridian, fights the heroines because she hates them personally due to a misunderstanding aided by some manipulation — but aside from that, she's a very sweet and naive person, so much so that the heroines have to pull punches against her...especially one of them, Cornelia Hale, who is Elyon's long-time friend. Good thing the misunderstandings are more or less cleared and they became friends again.
Charmcaster from Ben 10, the antithesis to Magical Girl Gwen. In the third series, Ben 10: Ultimate Alien, it turns out that her whole motive for being evil is to gain enough power to free her home dimension from a tyrannical being that killed her parents and left her lonely and bitter. She ends up developing a typical Magical Girl-Dark Magical Girl bond with Gwen as well, and even when she relapses later, Gwen is still insistent on helping her toward goodness.
Star Wars: The Clone Wars has Asajj Ventress. The only reason she fought for the Separatists seemed to be her starving for Dooku's approval, her greatest fear is being left with nothing, and she gradually turned away from the Dark Side, after Dooku abandoned her. The 'Magical Girl' she's foiling is Ahsoka, a jedi padawan with similar approval seeking from her own master.