The most important couple, borderline canon. The main story revolves around their relationship, and much of their actions and character development involves the other.
Homura's fixation on Madoka is infamous, not only in the anime but also portrayed in Oriko Magica manga, in Drama CD 1 'Memories of You', and Drama CD 2 'Sunny Day Life'. She follows her around constantly, thinks only of protecting Madoka and her happiness, and treats any threats to her with brutal efficiency.
In episode 8 Homura verbally admits to not giving a fuck about anyone who is not Madoka.
Homura threatens to kill Sayaka - and has real intent to do so - if the latter continues making Madoka sad.
Homura practically confessed to Madoka twice.
In Episode 8, she confronted Madoka right after saving the latter.
In Episode 11 we see another confession as well as a long, desperate hug. It also includes a Declaration of Protection, and these words, while Homura is crying:
Homura: To you, I haven't even known you for a month. I'm just some transfer student. But to me, you...
The different timelines show Madoka herself gets very affectionate with Homura, praising and glomping her, and indeed in the first timeline their roles are reversed, with the powerful Magical Girl Madoka protecting the sad, powerless Homura.
The naked space hugging scene is, if possible, more blatant on the DVDs. How? They took out the sparkles.
The entire Homura x Madoka bond is cast more romantically in the manga. After she heard of the dream Madoka had, Sayaka's mental image of them casts them as lovers.
Remember in episode 12, when Madoka finally left Homura after giving her her ribbon? In the manga, she takes Homura with her into godhood.
During Puella Magi Madoka Magica Portable, Madoka gets so attached to Moemura it can actually make her uncomfortable. Even after Homura drops the glasses and starts distancing herself, she can't stop Madoka from taking her home to meet her parents, who are quick to mention she's all Madoka talks about recently.
In a spin-off manga based on the Drama CDs, the second page features Homura wondering if, in order to appeal to the fanbase, they shouldn't make the whole manga into a rom-com starring Homura and Madoka. It even comes complete with a cute little comic about Homura coming home from work to her darling wife Madoka, who asks if she wants to have a bath or dinner, and Homura responding that she wants her. And then there's a little picture of the Naked Lesbian Space Hug. See for yourself.
In the Anicom magazine's 100 Questions, Madoka answers "Is there a boy you're thinking about?" by talking about how much mischief her little brother gets into. Then she describes her ideal husband as someone like her mother. In the PSP game, Junko mentions that Homura acts just like she did at that age.
Visitors to the Movic Madoka Magica exhibit got to hear Madoka gushing about how pretty Homura's hair is, and Kyubey telling Homura how Madoka thinks she'd look cute in glasses. Homura apparently goes red upon hearing this.
Plenty of official arts of these two hugging, dancing, holding hands lying on grass, Madoka looking at Homura in locker room, playing piano and singing together, building sand castles at the beach...
And then Shaft releases this◊. (Warning: massive Rebellion spoilers.) It's undeniable.
For Valentine's Day the mobile game released a short comic in which Homura gives Madoka chocolates claiming that she is her 'most precious person', and Madoka accepts them, saying that she also likes/loves (the word used is 'daisuki') Homura a lot. Hmm.
The same opening features Madoka and Homura in white dresses, lying in what seems to be water, reaching for each otherís hands with smiles on their faces.
In a scene in The Battle Pentagram, Madoka invites Homura to her home when the rest of her family is out, jokingly(?) asks her to bathe together, and gets Homura to sleep in the same bed as her, with Homura getting more flustered as the scene goes on. And then it gets better.
Homura: Hey, Madoka, are you still awake? Madoka: Yeah. Sleeping in the same bed is a bit embarrassing, huh. Homura: Thatís why I offered to sleep on the floor... Madoka: No, this is nice. Plus, youíre so warm. Homura: So are you, Madoka. Madoka: (laughs) Homura: Why did you invite me to spend the night? Madoka: When you told me you lived alone, you seemed so lonely. Homura: I... seemed lonely? Madoka: And so I kind of wanted to spend a lot of talking with you. Homura: Madoka... Um, thank you. Madoka: You shouldnít thank me for that. Iím so happy just spending time with you. Homura: Me too. Madoka: Can I sleep over at your place next time? Homura: S-sure. Thereís not much there, but if youíre okay with that... Madoka: Thatís not true. Youíre there.
Rebellion piles on the Ship Tease, but all of it has a nasty twist, bringing to the forefront how unhealthy their relationship truly is. A distraught Homura is comforted by Madoka, assuring her that she would never willingly leave her while she lovingly braids her hair, but this Madoka is one without the memories that drove her to her big sacrifice. Homura would do anything to protect Madoka from the Incubator, including willingly transforming into a witch. Madoka is delighted that she can finally bring Homura to heaven with her, but things don't go as planned. And at the end Homura declares all she wants is to ensure Madoka's happiness... by almost literally becoming the devil, forcibly dragging Madokami out of heaven, and rewriting reality to bring her back into the universe. Homura's universe. Homura explicitly says that her motivation for this is "Love".
Kyouko went from a psychotic Blood Knight perfectly willing to sacrifice innocent people, to someone who wants to believe again in justice and friendship and risks her life trying to saveSayaka, all in a few weeks, all because of Sayaka.
The mobile game includes a New Year's special with the cast visiting a shrine and picking omikuji. Everyone's fortune looks good...except Sayaka's, which says "the person you're waiting for won't come". Kyoko, trying to cheer her up, promises that she'll stay with her.
In Puella Magi Madoka Magica Portable, both Sayaka's and Homura's route, it's possible to prevent Sayaka's transformation into Oktavia. In Sayaka's route, this involves Kyoko comforting her after they learn the truth about soul gems. In Homura's route, it requires taking Kyoko to talk with her after the freak out - Kyoko is the only one who can get through to her. Not her childhood best friend, not her sempai, Kyoko.
A more light-hearted event: in the True Ending, Kyouko expresses jealousy when Sayaka comments on how perfect Mami is, and how she'd like to marry someone like her. Kyouko tells Sayaka it's not her fault that she's sloppy. When Sayaka asks why she's mad, Kyouko denies it in a tsundere fashion.
A less lighthearted event: You know how Kyouko has gone through complete and utter crap, yet still manages to stay human? Well, if Homura kills Oktavia before Kyouko and Madoka can attempt to save her, Kyouko realizes that there is no hope in the world, and those that do hope are only naive idiots like herself. And then she turns into a witch. That's right. It wasn't any of the aforementioned crap she went through that did it, it was someone who she knew for less than a month.
In Rebellion, the two are living together and argue Like an Old Married Couple on a regular basis (as this takes place in Homura's dream world, it seems she ships them too). During the battle against Homulily Sayaka outright states that the reason she returned from the Law of Cycles is that while she thought she left without regrets, she did regret leaving Kyouko behind, and they hold hands... a tender moment which is ruined by Nagisa squeeing about how much she loves cheese, which annoys Sayaka to no end.
Mami was intending to die with Sayaka, before Kyouko stopped her.
Madoka x Sayaka
Before Homura's past is revealed these two are by far the closest of the five. Sayaka's righteous nature stems from her constantly protecting the ever-timid Madoka, and Madoka's self-sacrificing nature comes from her guilt caused by Sayaka constantly protecting her. They explore and learn about the nature of Magical Girls together, and Madoka's fall into despair closely mirrors Sayaka's.
In Episode 1, Sayaka say to Madoka "I'll make you my bride!", though the scene is only a joke between friends.
In their Max Relationship scene in The Battle Pentagram, Madoka expresses how scared she is for Sayaka, tells Sayaka that if it weren't for her she wouldn't have lasted this long, and outright tells Sayaka she loves her. Sayaka tries to blow it off by saying Madoka should say that to a boy she likes, but that doesn't stop her from cuddling Madoka, telling her how nice she feels and smells, and asks if they can stay like that for a while.
While Kyouko is normally rather savage, aloof and antagonistic towards most people, all of her interactions with Madoka involve Kyouko being kind, caring, and even encouraging Madoka to do "the right thing". Kyouko helped Madoka save Sayaka, because Sayaka is her best friend, and even brought Madoka Sayaka's dead body, expressed pain when the girl grieved over her, and yelled at Homura when Homura was all cold and callous over the situation.
Homura and Sayaka
However brief it was, near the end of Rebellion, Homura gets up close and violates Sayaka's personal space, and stares at her breasts for a few seconds.
Gen Urobuchi (series writer) said in an Madoka Magica interview (see Black Past) that he believes in same-sex relationships, and that they are not different than any man-woman relationship. He also said that if he wanted, he could write a BL story next.
One of his other works, Fate/Zero, features its own level of Ho Yay, between both male and female pairs.
In another interview, Gen revealed Madoka Magica was started and revolved around the concept "where Homura saves Madoka". Yuri is the pivotal idea of the franchise!
Ume Aoki (original character designer) and Hanokage (manga adaptation artist) ship Homu/Mado and Kyou/Saya.
Following the Different Story manga, Hanokage suggests thisOT3 could inspire "infinite possibilities".