The entire Monica request. At the start of the game, Monica bites Micah at every turn, and generally acts hostile to strangers out of nervousness. Shara asks Micah to help Monica by pretending to be "the Rose Prince", from Monica's favorite fairytale. Obviously, Monica is less than impressed, but after taking her out to the various dating spots, she eventually opens up to Micah and does a complete 180 personality-wise. Afterwards, she acts cheerful, openly talks to people, and even offers to bake Micah a cake. D'aww.
Raven's whole quest sequence, which ends with her revealing she's half-phoenix and looking just so Woobie-ish and sad. So what does Micah do? Reveals he's also half-monster, tells her she's not alone anymore, and considering how popular she is with fans, quite possibly marries her on one of his two files. Closest thing you can get to reaching through your DS and hugging her.
Near the end of her seventh quest:
Raven: (crying) I thought you disappeared...
Micah: (hugs her) You see? I'm right here. I didn't disappear.
But the way Micah comforts her and tells her she's fine just the way she is and gives her a hug most definitely is.
ANY request with ANY girl later on. Bonus points for the engagement scenes.
Daria's "Dream" request, where she tells Micah about a fond memory of her dad taking her on a trip, and that that's why she wants to cover the world with her art.
If the player marries her and takes her on a date to Rainbow Falls, she'll confess that she was afraid to marry him because of the possibility she'd outlive him. Micah promises that even if she does, all she has to do is think of him and he'll be with her forever. Daria is moved to tears.