The twins' reunion in Frost Bites, after Edgar had briefly thought Ellen dead. For some reason, the text doesn't mention the hug they share, but an illustration shows it, and it is glorious. Destruction is raining down around them, and they don't even care.
Their reunion in Split Ends as well, although the dramatic tension is considerably lightened by their exchange beforehand.
Heimertz and Dahlia's wedding in Hot Air. These two went through a lot to get to this point.
The Animated Series
In The Great Edgarini, Edgar shows the class his amazing escape artist skills and becomes popular. The truth is, the popular kids are just using him for their amusement, but he wont listen to Ellen trying to warn him about it. The popular kids try to humiliate Edgar in public, but Ellen shows up and saves him despite him being rude to her earlier because of his popularity. Edgar is forced to make a choice between humiliating Ellen or losing his popularity, and he chooses the latter.
In "Crushed", after Edgar finds out the truth about Ursula, Ellen finds him lying in bed dejectedly and tries to comfort him. Later, as the twins watch Ursula getting her comeuppance, Edgar concludes that his most prized possession isn't his satchel... it's his sister.