Both seasons end on these; honorable mentions include William Baxter's story and Stoner's "Pacific State" photo of Renton and Eureka (see on the main page).
After Eureka begins to show more and more Coralian features that physically start to change her body, she becomes afraid of what Renton and the kids would think of her. Instead of being frightened, however, Renton compliments Eureka's newly formed wings by telling her that she looks beautiful with them. Cue Eureka giving Renton a huge hug.
"Our papa is the only one who can save our mama!"
The entire last episode counts as this.
Specifically when Renton and Eureka FINALLY kiss and promptly save the world with The Power of Love and later in the epilogue where a year has passed with Axel and the three kids are shown to be wishing upon a star while looking at the moon (which has a heart carved into it with Renton and Eureka's names inside) eagerly waiting for Renton and Eureka's return. Cue the camera zooming outward to a not-too-far-off forest where we see Renton and Eureka together.
Late in the series, when Will B. Baxter's wife recovers just in time to see him again before they're both taken to be with the Coralians until Humanity is ready to come together again. In fact, the opening scenes of that episode are all pretty heartwarming (with a bit of Tear Jerker mixed in); A similar scene took place between a young girl who had just recovered from Desperation's disease and her parents.
After Eureka tried putting on makeup (and by tried I mean slathered it on) to impress Renton, everyone is horrified by how she looks and she even makes the kids cry. The laughter quickly subsides when Eureka runs out of the room out of shame and Renton chases after her. When Renton finally catches up to her and she tells him that she only wore it to make herself look pretty to him, Renton tells her that she looks pretty without makeup and FINALLY tells Eureka that he loves her.. Awwwwww.
In fact, episode 25, as a whole, too. Will B. Baxter's tireless work as The Caretaker for his wife, his and her Back Story, and the advice he gave to Renton are all very touching.
Also, when Renton met back up with Eureka in episode 26, after abandoning the Gekko several episodes earlier.
And Renton and Eureka scoring the crew's only goal in their soccer game.
When Dominic and Anemone were reunited in episode 48, admitting that they love each other for the first time. They do this while upside down, in FREEFALL.
Anemone: Somehow I feel like I wouldn't care if I died right now. No, that was a lie. I want to live... together with you, always.
Axel: "Yes hurry and come back with that young lady of yours Renton. Your lovely children are waiting for you." Cue the camera zooming out to a not-so-far-off forest where Renton and Eureka are seen together.
When Talho tells Holland that she's pregnant. Holland panics because they're about to go on a dangerous mission that Talho has to be present for, showing a side of him not often seen, one that's loving and supportive and worries about the people he loves. Talho, of course, insists on coming anyway, but it's this moment that really shows both how much they love each other and how much they have grown and changed, into dependable teamparents of sorts as apposed to the insecure immature people they were before Character Development kicked in.
Episode 49, when Jurgens and his crew decide to act as the Gekkostate's shield against an entire army armada. Specifically, Jurgen's little speech:
Jurgens: Therefore, I want you to take care of Dominic and Anemone. Those two are our comrades! Freeing up a future for the two of them isn't such a bad thing, eh?