All five of the rose duelists - together in the same scene for the first time - waiting together and hoping for Utena's victory
Considering how screwed up Saionji and Touga's relationship is - what with Touga getting him in trouble to get closer to Utena, teasing Saionji over their past better relationship, and the implication that Saionji abuses Anthy and hurts Wakaba as a way of dealing not only with the pain Touga caused him, but a way of surpressing his desire to fix their relationship - seeing Saionji not only move past this but reconcile with Touga in the last arc, and become friends again in the epilogue is pretty sweet from two otherwise horrible characters.
Saionji being angry at the mention of his and Touga's past friendship, but when the camera pans to his desk you see that, despite everything, he still keeps a photo of them together.
Utena (crying): Himemiya! At last! We finally meet.
Episode 34: "Then I'll become her prince! I'll become her prince and save her!"
After the infamous Cantarella scene in episode 37, in which Anthy and Utena both claim to have poisoned the other, they partake in their treats anyway.
Anthy: This tea is delicious.
Utena: So is this cookie.
Utena to Anthy in episode 37 "In ten years, we'll laugh together and have tea." They then intertwine their fingers together when holding hands. And Utena next saves Anthy from her suicide attempt telling her she thought they were going to "laugh together and have tea ten years from now!" Anthy breaks down in tears, apologizing.
The last lines Utena has with Touga and Saionji too. They claim people who believe in truefriendship are fools to which she happily declares "Don't you know? I ama fool".
In episode 12 Wakaba brings Utena out of her Heroic B.S.O.D.. It was also nice to see Anthy show some attachment, some emotion toward Utena other than generic happiness, even though she was still technically Touga's "Rose Bride". And when Utena wins the duel against Touga and wins Anthy back Anthy begins to state her usual Rose Bride spiel but Utena tells her she doesn't have to say it and says they should just go home together while offering her a warm smile. Anthy smiles back.
During the Black Rose arc Wakaba is the only one who Utena did not let fall to the ground. Best friend indeed.
Episode 18, Nanami to Mitsuru "Don't be silly, you shouldn't think that. you don't have to be a grownup! I like you just the way you are." Considering how stuck up Nanami usually is, it's nice to see her treat Mitsuru like more than just a servant.
Saionji actually behaving other than a plain Jerkass and making a hairclip for Wakaba to thank her for her hospitality (Episode 20). He leaves and the clip ends up with Anthy, but it was still sweet.
Near the end of the last episode which subtly shows that the cast has improved their relationships (Kozue at the piano showing that the relationship between her and her brother was changing, Shiori in the fencing club showing that her relationship with Juri has changed, etc) and may be able to grow up into healthy adults after all. A revolution has occurred indeed.
In a similar vein, the badminton scene from episode 37. It's one of the few times Utena and various student council members are shown just interacting as friends, and their jokes seem to indicate that they are moving past some of their personal problems.
Utena: Someday, together...
Anthy: Someday, together...?
The very last shot you see in the whole series is a photo of Utena and Anthy's hands intertwined.
In the manga, Kozue's jealousy of Miki and other girls is portrayed as a bratty, insecure girl afraid to lose her twin rather than a disturbed girl seeking attention from him by sleeping with dangerous older men. The chapter focusing on the Kaoru siblings has her kidnapped by End of the World, and Miki must win his duel with Utena to save her. Utena wins, but Kozue is freed from her prison anyway and the siblings tearfully embrace with Miki declaring he's glad she's safe as she tries to apologize.
Juri's friendship with Miki in the anime is one of the only healthy relationships in the series. Both of them are messed up with a ton of projection issues, but Miki is very respectful to her as a person and not just his fencing captain, while Juri is much warmer to him than she is to most people.
In the manga, seeing Touga not be a complete jerk and actually revealing just how much he loved Utena and her ideals.
The entirety of the episode where Nanami thinks she's laid an egg is this. It's wonderful to see how much Nanami truly cares for it.