"Ghost: The Phantom of Daten City", featuring Stocking falling in love with a Ghost.
To expand on that, this particular Ghost disgusted just about everyone except for Stocking. She was the only one who stood up for him when everyone hated him, and he subsequently fell in love with her. His proposal to Stocking, and the revelation that he couldn't move on from this world until he discovered love, is one of the show's biggest tear-jerking moments yet.
Quite possibly the biggest tearjerker moment in the episode was Stocking tearfully proclaiming that she was willing to give up heaven for him. Quite literally saying to him You Are Worth Hell.
Panty sticking up for Stocking, too. She even mentioned how there were more important things than sex.
Personally, this troper found it sweet when Panty actually displayed a Big Sister Instinct, not only wanting to prevent Stocking from dating a Ghost, but also because she's concerned about her and wants better for her. The episode even opened with her trying to find a guy good enough for her and even spends the entire episode trying to convince her that he isn't worth it, especially since he's a Ghost. She even pulls off a Knight Templar Big Sister when Stocking decides to elope with the Ghost. Mostly heartwarming because she usually doesn't show this side, especially to her sister.
Panty eventually falling for Brief in Panty + Brief.
Brief:[inside abandoned shack with Panty] We should be safe here. [beat]
Panty:[holds Brief's hand]
Panty: Something's wrong with me...
Brief: D-don't worry! I'll protect you! Because I love you! Ever since I saw you in school...[Panty gently lays Brief on bed]
Panty: Geek Boy, let me see your face. [pulls back Brief's hair]
The fact alone that regardless of how much flack and abuse he got from Panty, Brief stayed loyal to her, helped her out when she lost her powers, and legitimately cared for her well being. And it managed to pay off. D'awwwwwww.
Their interrupted lovemaking session near the end of the episode also qualifies.
Particularly since it's the first time Panty has truly made love to somebody, as opposed to "having sex" or "fucking someone" as is usual with her.
The fact that the two left behind their autographs for Terao's daughter at the end of Episode 5 was kind of sweet, even if they were kind of pricks otherwise.
" Don't you want to be my thousandth? Though honestly...with the way I am now, you're actually gonna be my first, Brief."
It's a shame their relationship basically returns to the way it was afterward; however, from that point forward, Panty no longer called him "Geek Boy" even when making fun of him.
The episode "Nothing To Room" because the Anarchy siblings weren't fighting with each other and acted like best friends.
Panty: So let's say we get this bigass pole, like it's really fuckin' long, right? Then we stick that shit onto the Earth like this, see? [places pole on a basketball Stocking's holding, then grabs Bonekitty] This is you. Now pay attention. [imitating Stocking] "God dammit, what is that pole?!" And you start walking up it like anyone would do and are like, "Where the fuck does it go?!", so you just keep going higher and higher until guess what?! ...C'mon, you're not guessing! Gimme something to work with! ANYTIME, STOCKIN'!
A bit of Fridge Logic with this... But, in spite of how much they fight, Panty trusts Stocking with her second gun, and when she needs it Stocking will give it to her without needing to be told.