In Episode 5, Madoka expresses concern about Sayaka becoming a Magical Girlparticularly after what happened to Mami. Sayaka brushes her off saying that if she hadn't then she would have lost Madoka and Hitomi which she finds to be even scarier and assures Madoka that she wont need to contract because she will protect the city now. It's a Heartwarming moment since it shows just much Sayaka values her friends and ideals that she was willing to sign on to what she knew was a dangerous job.
Sayaka bringing up the newly-healed Kyosuke up to the roof for a impromptu concert. Kyosuke's parents, nurses, and doctors are all there to see him play his violin again, and you can tell that everyone present knows that they're in the presence of a true miracle. Putting aside her friend's rescue, this one event convinces Sayaka that "There's no way I'll ever regret it".
In Episode 7 Kyoko takes Sayaka to her family's old church and tells Sayaka her backstory and why she became a Magical Girl. She wanted to cheer Sayaka after she learned that her soul gem is a Soul Jar and to give her advice on being a magical girl. While Sayaka does decline her offer of becoming more selfish she does apologize for judging her earlier.
In Episode 8 Kyoko saves Sayaka from Homura even though it went against her policy of helping people. Later on both of them meet up in the subway station and Kyoko's line implies that she went through the trouble of looking for Sayaka all over town. It seems that Kyoko considers Sayaka her friend.
In Episode 9, Kyoko performing a Mercy Kill on Witch!Sayaka, along with a Heroic Sacrifice. Not because Sayaka couldn't be defeated without one, but because she didn't want Sayaka to die alone.
Kyoko and Madoka's talks give the girls some sweet bonding time.
In Episode 10, Homura swears to repeat her time-travelling 'eternal maze' as many times as it takes to save Madoka, her only friend. This is after you see what led her to be so cold in this version of the timeline...
Timeline 2 starts off as a series of these for Homura. In her second introduction to Madoka she expresses joy at seeing her friend alive again, she's accepted into Mami's Magical Girl team and then she kills her first witch. Theses are the only times we ever see Homura truly happy in contrast to her usual stoic self in the show until the finale.
Afterwards, Sayaka and Madoka being able to share one last talk before passing on (or ascending to a higher plane of existence depending on how you look at it), which makes Sayaka's fate a little less bitter. (Thank God Kyosuke is shown later recalling her when he's back to music.)
Meta example, with a bit of Foreshadowing: Remember how Urobochi mentioned his tragedy syndrome in the quotes section? And how the protagonists overcoming it would require a fundamental change in the universe they were in? You finally got that happy ending you wanted, Urobuchi. Good for you.
Homura, near the end: "Would you like them?" With everything those ribbons must have meant to her, she still offered them freely and happily, with the most gentle smile. After all the horror and anguish she struggled through, Homura Akemi found peace.
Madoka's little brother Tatsuya loving his sister enough to remember her, despite the fact that he's barely a toddler and hadn't been at all involved in the Magical Girl stuff. That's right, his love for his big sister is powerful enough to survive a complete and utter rewrite of the world—just because she was his sister.
One hopes that as he grows, Tatsuya and Homura become close, and can share memories of Madoka... together.
The scene where Madoka goes up against Walpurgisnacht, telling the colossal witch, "It's alright now. You don't have to hate anyone anymore and you don't have to curse anyone anymore either. I'll go back before you turned into this and take the burden of all your pain."
In the final scene just before the credits, Homura steps up to fight a horde of Wraiths, and she pulls out a bow. Madoka's bow. She doesn't have the time-changing shield anymore. She doesn't need it anymore.
"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."
The whole episode can be summed up into one quote:
"Don't forget. Always, somewhere, someone is fighting for you. As long as you remember her, you are not alone."
The end of the Madoka manga. After the normal ending, there are a few extra pages; Madoka and Homura, who is once again bespectacled and twin-braided, implying all her mental trauma is a thing of the past. Homura apologizes for being such a gloomy friend, and Madoka laughs, assuring her that the two of them will be friends forever.
The various endings in Grief Syndrome. In either ending where Sayaka dies, it shows Kyoko and Oktavia (Sayaka's witch form) getting along just fine. Also, there are two endings that require the survival of two characters: Madoka / Homura and Sayaka / Kyoko, respectively. They're wedding scenes.