Spoiler Warning: The following article contains spoilers of both the series Puella Magi Madoka Magica and the movies, especially Rebellion. I strongly recommend that you watch the series and the movie Rebellion prior to reading this.
Homura Akemi is a rather complex character with a central role in the story of Puella Magi Madoka Magica. In some ways, she makes the plot, because her time traveling is what causes more "lines of fate" to become attracted to Madoka, increasing her potential power as a magical girl.
In many ways, she is set up from the beginning of the series as an adversary to Kyubey. But what is ambiguous is whether this makes her good or evil, largely because it's unclear whether Kyubey in the show is good, evil, or something else altogether that humans cannot truly comprehend. In the movie Rebellion, her actions are even harder to read in terms of whether they're morally justified or not.
Sayaka: You look like someone who's given up on everything. When you talk, you use empty words. In fact, you're doing it now. You say you want to help me, but I know that's not what you're really thinking. You're not fooling anyone. Uh-uh.
Homura: Do you realize that you're just making Madoka suffer more and more?
Sayaka: Madoka? This has nothing to do with her.
Homura: You're wrong. Everything has to do with her.
Who is Homura Akemi?
Homura is first introduced as a mysterious character, who opposes Kyubey and seeks to warn against becoming a magical girl. But, since the main viewpoint characters Madoka and Sayaka have no reason to think anything bad about Kyubey, they are immediately suspicious of Homura. What's weird is, having never met her before, Madoka thinks she saw Homura in a dream.
Homura first meets Madoka in school, and pulls her out of class to talk, giving her a vague warning against changing her life.
Homura later shows up to try to help Mami fight a witch. But Mami is suspicious of Homura and ties her up, fighting witch alone, with disastrous consequences.
Homura is later the only one able to save magical-girl Sayaka from dying when her soul gem is thrown away, because she's the only one who knows what a soul gem's significance is (that it actually contains the girls' souls). At this point, it's unclear how, but it's certain that Homura somehow possesses knowledge about being a magical girl beyond what even Mami knew.
Then, it's revealed that Homura is gearing up for an event she knows will occur in the near future called Walpurgis Night. On that night, a dangerously powerful witch will come, and she wants to defeat it without Madoka having to become a magical girl. Her plans, powers, and motivations are mysterious.
Mysterious at least, until Homura's past is revealed:
In her original timeline, she was a weak girl, coming back to school after having been briefly hospitalized.
She had trouble making friends because she was shy, and had missed so much class that she was struggling to keep up with everyone else.
In that timeline, Madoka and Mami were already magical girls, and they became her friends.
But by the time Walpurgis Night came, Madoka was close to dying, when Homura wished to be strong enough to protect her and became a magical girl.
This instantly sent Homura back in time about a month, allowing her to relive her time as Madoka's friend. She set two goals: defeating Walpurgis by herself, and preventing Madoka from making a contract and becoming a magical girl.
Homura tries and tries, getting stronger each time, but she's never able to do either goal, so she keeps having to go back in time to try once more, to relive the same month, with the hopes that this time, she will get it right and be able to save Madoka.
Then, Madoka finally makes a wish, to erase all witches from history, and the present, and the future. When this wish is granted, it seems that Madoka herself is the one appointed to enforcing this new world order; she essentially becomes a goddess, recreating the entire history of humanity according to a vision she considers more just.
There's only one problem, Homura. Homura worked in all those timelines, over and over and over again, to save Madoka, and then Madoka ups and Jesuses it up, leaving her on Earth without any of that sweet, sweet, middle school ass to love.
So while the first two Madoka Magica movies are just a retelling of the story of the anime with slight differences, the third movie, Rebellion, is about essentially the aftermath of Madoka's new world order when it comes to Homura's psychology. She doesn't think living in a world without Madoka is fair even if the Utopia Justifies the Means.
The movie Rebellion begins with Homura and pals alive and well and acting as magical girls again. They're looking cheerful, albeit every bit as creepily animated as before. It seems like it's an ideal world for all of them, as created by Madoka' new veto on the whole "becoming witches" thing.
Except... Madoka's in this new world too? And, no one but Homura knows anything about what happened before? Strange.
The truth is, Homura is basically being deceived by her own nearly-a-witch mind. She ends up breaking out of her own hallucination-land, and it's revealed that she has been kept in a nearly-a-witch state and unconscious so that Kyubey can entrap Madoka (but it's For Science!).
Homura goes, "hell naw, I do what I want", and becomes something like an Anti-God to Madoka's God, not necessarily evil, but definitely rebellious against God's new order, hence the title of the movie, Rebellion.
Even though witches aren't born into this world anymore, that doesn't mean the curses of the world have completely disappeared. They just changed their form is all. And now, they attack us from the shadows. This world isn't worth saving. Tragedy and sadness will never truly disappear. But even so, it's the place she once tried to protect. I remember that and I will never, ever forget it. That's why... I keep fighting.
— Homura Akemi
Is Homura Good or Bad?
This issue has caused more than a small amount of debate among anime fans and critics.
What are Homura's motivations and intentions?
Is she a good person?
Are her actions reasonable?
Does she even love Madoka, or is she just obsessive about her?
One could see Homura as having the time-travel version of Homer's Odyssey, even her name sounds like a feminine Japanese equivalent of "Homer".
In the Odyssey, Odysseus takes years to return home after already spending a lot of time away in the Trojan war. Magic and mundane forces alike conspire to keep him from making it home, and he almost gives into despair thinking that this will never happen.
Similarly, Kyubey tries to block Homura in the series from fulfilling her wish. Whether Kyubey is evil or not, she sees him as such, because he wants to manipulate Madoka into becoming a magical girl. This is something Homura knows means slavery, watching friends die, not being able to have a normal life, losing control of one's very soul, and even being bound to one day become the thing magical girls fight; a witch.
She can be seen as similar to another figure in Greek storytelling; Cassandra. Cassandra was a prophetess, but she was cursed that no one would ever believe what she prophesied, even though it would always come true. Similarly, Homura lives with this knowledge about what being a magical girl entails, and how it is a trap put there by an alien who is just using humanity. Her problem is, she has a lot of trouble getting anyone to listen to her. She has to watch friends die over and over again in many timelines, because she cannot get them to heed her warnings.
Given all this trauma she goes through, it's not surprising that Homura goes near to becoming a witch in Rebellion, despite the fact that the "battle is won" in the sense that Madoka is saved, and magical girls no longer turn into witches.
The problem for Homura is the absence of Madoka. She envisions a "perfect" Madoka to be a Sailor Moon-esque champion of purity and justice, and envisions a good world wherein all of her magical girl friends save the day. But then she realizes that this sweet reality is a lie, it is in fact her lie to herself.
Some people may see Homura as evil, or at the very least, not truly motivated by love of Madoka at all. She seems to see Madoka like a maiden to be rescued, and, other than Madoka's initial kindness to Homura in the original timeline, there just isn't that much between them to logically prompt the kind of love that makes Homura time-travel so many times.
She may be motivated purely by anger at Kyubey, for what happens to all magical girls. A desire for justice. It may be that she's really going back in time to try to thwart or even destroy Kyubey once and for all.
One example that could be evidence of this is in the first encounter Madoka has with Kyubey, Homura is trying to chase down and shoot Kyubey. Why? That makes little sense if her real goal is, as her stated wish, to protect Madoka. It also seems weird she should know from her experience that you cannot defeat Kyubey by shooting him, as not only can he regenerate his body, but shouldn't she know that Kyubey is actually not one but many, an alien race possessing a single hive mind?
Perhaps she was simply trying to take down Kyubey all along, and is only pretending her wish is for a less vengeful reason, by saying that it's about love. Is Homura an unreliable narrator in her own recounting of her timelines in the show? Or perhaps she is in love with Madoka, but it's an obsessive, dangerous, stalker-y kind of love, and very one-sided.
Having Homura be secretly more selfish, obsessive, petty, or vengeful than she claims to be would fit with the series' overarching theme of "no one is selfless".
Whether Homura is right or wrong in the end depends heavily on whether Kyubey is right or wrong. He's much like the snake in the garden of Eden; tempting girls with forbidden things; in this case both magical abilities AND the granting of one wish, whatever their heart's desire is. While he may have a good reason for what he's doing, his methods are unethical, at least, by human standards of ethics. Informed consent is not high on his list of priorities. Kyubey doesn't understand human emotions, and doesn't know why we consider his methods of saving the universe from entropy to be wrong. Throughout all of human history, Kyubey has been preying on humans who, out of weakness or ignorance, were never able to challenge his rules, until Madoka and Homura show up.
So, is Homura a fallen angel figure, corrupted by despair and abandonment?
Or, is she a crusader for justice and truth, hoping to set Earth free from the tyranny of the Incubators for all of time, something that Madoka was too compassionate to do?
Did she choose what she chose because she saw that Madoka was unhappy and was truly in love with her? Is she just obsessive and envious? That's up to you, the audience.
With the popularity of this franchise, maybe future animated material based on all these new mangas they're doing of these characters will also explore the issue of Homura's character.
As for me, all I can say is that Homura seemed like she was very much in love with Madoka, and very much ultimately hurt by the way things turned out at the end of Puella Magi Madoka Magica.
Will she become a truly evil being? Only additional movies, anime episodes or manga will tell.