In "Ice Station Sabrina", Sabrina was willing to risk using her magic in front of Brad rather than allowing Brad, Harvey, and Salem to die in a collapsing fire tower. (She even explicitly says, "I gotta save you guys; I don't care what happens to me.") This troper found that particularly heartwarming.
Near the end of the series, Salem goes into full-on Sincerity Mode about how much he cares about Sabrina's well-being and happiness. All the while, he doesn't lose his usual catlike tone of voice, which if anything makes it seem even more sincere than if he'd tried to sound sincere. Also poignant because he's the only character besides Sabrina to remain a regular for the entire series—no one else has been with her that long, so he should be the one to make that speech.
The Season 1 episode where Sabrina takes a test to see if what she feels for Harvey is really true love. It turns out to be right, and the episode ends with the two kissing in the car as fireworks go off. Salem and Zelda watch them from the porch.
Salem: I still can't believe you let her take that risk.
Zelda: At sixteen, it's always true love.
Heartwarming in Hindsight as the series ends with The Reveal that Harvey and Sabrina are soul mates, and they end up together. What's more is that he now knows the truth about her being a witch and is completely accepting of it.
Their reunion at the very end of the series. Big Damn Kiss as the others look on.
The Friday the 13th episode - Sabrina learns there's a loophole that she can tell a mortal her secret for the day (and their memories will be erased at midnight). Her aunts didn't tell her because of their bad experiences with telling mortals. Nonetheless Sabrina confesses first to Valerie - who finds it so cool. There's a Good-Times Montage of Sabrina entertaining Valerie with her magic - the whole time looking so happy that she can share the secret with her best friend. Harvey is told too and he finds it just as cool.
Libby discovers the secret too and offers Valerie the chance to be popular if she backs her up to the news. Despite her desire to be popular, Valerie sides with Sabrina. Despite her wannabe nature, she was a true friend.
The aunts don't find this out until the end of the episode, prompting this exchange.
Sabrina: You're right. I don't feel the same way about Harvey or Valerie anymore.
The two aunts tense up, preparing to comfort Sabrina, thinking she's had a bad day.
Sabrina: I like them so much more.
She shows them pictures taken in the Other Realm.
Libby's softer side is revealed - she is implied to have a very loving relationship with her grandmother. Notably Sabrina pretends that she wants to visit her own grandmother, Libby agrees to help her with the parade float (albeit in a Tsundere sort of way).
Sabrina's Pet the Dog moment to Libby in Season 2's Christmas Episode. She spends the whole episode getting tortured by her Bratty Half-Pint of a stepbrother - which is Played for Laughs most of the time. But when Sabrina acts as Santa, she points her finger at Libby's house. Cut to the stepbrother giving Libby a handmade jewellery box with her name on it. Libby is unambiguously moved by this.
In “Boy Was My Face Red”, after Sabrina gets humiliated and people are laughing at her, Gordie helps her get up after she trips and quickly gets her out of the school. He is also the only one who shows any pity and comfort for her since he knows what it’s like to be laughed at.
Season 2's Halloween Episode. After the chaos at the party dies down, the guests think all the crazy Other Realm stuff was All Part of the Show and Sabrina conjures up the 10,000 Maniacs to perform "Rainy Day" - with a sweet sequence of all the characters dancing to the music.
"Sabrina and the Beast" - despite being initially repulsed by Harvey's new beast form, Sabrina decides to spend time with him anyway. They enjoy each other's company and she legitimately forgets that he's a beast. This gives her the realisation that she loves him for who he is; not what he looks like.