The snowball fight. This is apparently Carpenter family tradition (informally). And not only do the kids decide that Harry's a legitimate target, but so does Charity - even she's decided he's family by this point.
Combined with Tear Jerker: After Michael's been shot during their escape from the Denarius he tries to leave Molly and Charity alone to wait for news on his surgery. Charity, crying but still proud calls Harry by his first name for possibly the first time since she was introduced:
Charity:Families stay, Harry. He would stay for you.
When Ivy, Harry and company are meeting the big Nasties at the local aquarium she goes missing for a few minutes. Harry quickly figures out where she is, though: watching the otters at play. Because Ivy may be the repository for all human knowledge, but she's still an eleven-year-old girl, and otters are cute.
When the Archive is kidnapped and Dresden writes her a note.
Michael gets these all the time but one that really stands out doubles as a moment of awesome as well. After he was shot and had some of his organs shredded by a fallen angel shooting him and spending hours if not days in the hospital in critical condition. The first thing he does after waking up is ask if Harry was okay.
One in Small Favor that really got me: during the hob attack in the subway, Harry and Michael burst into a room where an attendant ushered some trapped travellers to protect them, and is furiously praying for help and protection. When Michael, Knight of the Cross, busts in with a shining holy blade emitting pure white light, she begins crying tears of shocked, hopeful joy, to which Michael replies, "Of course He is there. Of course He is listening. Granted, He doesn't always answer this quickly..." The quiet power and beauty of that one scene, where amidst all the horror and Grim Dark of the Dresden Files, the heroic Knight in Shining Armor really does show up to save the day, and the effect he has on the ordinary people, always makes me want to cry. That one paragraph summed up everything you need to know about the Knights of the Cross and what they do, and firmly and forever cements them as the unquestioned Good Guys in an otherwise very grey setting.
Later on, when Harry is having his mental breakdown when he learns that Mab had taken his blasting rod and Mindraped him into not remembering it, Michael leans down over him and prays to break the enchantment....and the power of either God or simple faith in that prayer is enough to utterly shatter the geas on Harry's mind. Really shows both the power of Michael's friendship toward Harry and the strength of his faith, as well as the raw power of good in a setting overrun by evil.
There's a moment near the end after Michael has been badly wounded and is in the hospital, Harry tries to leave Charity and Molly to wait for news without him, given that he thought they would be mad at him. Charity grabs him and tells him that "family stays." Given Harry's relationship with Charity (one of unmitigated anger from her towards him) its pretty touching. Esepcially considering she calls him 'Harry' instead of 'Dresden' for possibly the first time since her introduction.
Not to mention the moment when we learn that Michael will be too impaired by injuries to be a Knight any longer ... and that it's the best possible outcome for his career as one, because he'll be able to retire honorably and stay home with his family, rather than fight on and on until he dies.
Not all heartwarming moments must be between friends. After the chaos on the island, after all the mind games and traitors and manipulating, Harry's conversation with Eldest Gruff is so gloriously honest it melts the heart.
"They tell children stories about you guys, you know," I said. "Still?" he said.
And still, the one attacking Harry makes it clear he does this with severe reservations. He greatly respects Harry for his wisdom and ability to even out gambit some of the oldest Fae. Had it not been a direct order, he likely wouldn't have taken the job. And then when Harry offers him a loophole to keep him from smiting Harry, he gladly accepts it.
It's a small thing, and often overlooked but. After Harry tells Michael that Lash is dead and gone Michael is at first skeptical, knowing the Fallen the way he does it's understandable. But when Harry opens up and explains just what happened (something he had only done with Murphy so far) Michael believes him, completely.