Amazingly, Nyanko-Sensei gets one when he helps a lost little girl back to safety - carrying her on his back in his One-Winged Angel form. His seemingly unkind and blunt attitude really isn't fooling anyone by this point, is it?
And right after that, when he reunites with Natsume after their fight and his being kicked out of the house—"Natsumeeeeeee!" (Cue the big fat kitty galloping after his "pet.")
Give Natsume access to a Youkai which is helpless, depressed, or otherwise in pain, particularly one that's even vaguely cute. Watch the fangirls melt at how adorable he becomes when he's got something to protect.
And then there's Natsume with Tama-chan... just... oh, goodness, Tama-chan!
In episode seven of the Oddly Named SequelZoku - What initially seems to be a cruel prank by Reiko (taking a Youkai who's name she had stolen's contract and tying it to a tree branch, telling him not to come back for it for fifty years "or else the seas would rage and the world would be destroyed!") turns out to be an incredibly sweet gesture: The little Youkai wanted to see the sea, but was afraid to leave the forest. Reiko knew that fifty years was but a blink of an eye for a Youkai, and that if she tied the contract to a tree, then by the time the Youkai came back for his name, it would be tall enough for him to see through the forest -to the ocean beyond.
In San, Natsume and a cat/prankster youkai from his childhood apologizing and coming to terms with one another.
Natsume's conversation with Tanuma after the latter is attacked by a dangerous youkai while trying to help Natsume. Aside from the Ho Yay, Natsume realizes that, although he should never lose his concern for his friends, he should be more confiding in them (or at least Tanuma).
The ending of the Moon-Splitting Festival arc, when Houzuki and Fudzuki leave the mountain side-by-side as two identical lights.
Chapters 51.1 and 51.2 of the manga, detailing how first Nishimura and then Kitamoto befriended Natsume. Nishimura was probably Natsume's first real, human friend, despite often just being cast as one of Those Two Guys with Kitamoto.
In chapter 52, when Natori tell Natsume that in the past, he wanted him as an ally to help his cause, but now he is happy to help Natsume however he can.
Chapter 56 of the manga, the ending when it seems as if a little girl-youkai is going to vanish to wherever youkai vanish to after fulfilling her mission of returning a towel to a human who was able to see her only once, fifty years before. Natsume gives her a gift of a new towel from the now-old man, and she re-materializes, smiling in obvious glee.
In the same chapter, before that, she realizes how little she knows about humans. She first expresses concern that Natsume might die just from being out in the rain, and then worriedly asks Natsume whether after fifty years, the man is still alive. He is, and he is now a grandfather.
In episode 5 of season two, you learn that a friend of Natsume's friend had a grandfather named Shin'ichiro that believed in Youkai and wanted to see them, as well as that there were Youkai that would often come to visit him and watch him learn about them as a way to entertain themselves. At the end of the episode, not only do these Youkai help save Natsume from an evil ayakashi, but you also see that when Shin'ichiro was on his deathbed, they gathered around him and performed a healing spell in the hopes of making him feel better.
In season two of the anime, you find out that there was one young human boy that did not fear Reiko. When he sees two other boys making fun of her, she has to stop him from going after them with a baseball bat. Reiko even exorcises a malicious Youkai from the boy's home because she cares about him so much. Many years later, this man adopts Natsume, becoming the first to fully accept the Youkai-seer into his home. This home is the very same one Reiko protected years before, and Natsume eventually does the same, finishing the job this time.
Chapter 31 has the flashback where Natsume was adopted by the Fujiwara couple. They were the first people to even want Natsume to live with them and their kindness pulls Natsume out of his Despair Event Horizon.
The big finale of Season 4, as Nyanko-sensei accompanied Natsume on his long, long trip back to visit his old home. They at long last arrive at the warm hours of twilight. As Natsume began reminiscing about the short time he had spent in this place, even Nyanko-sensei, in complete contrast to his usual loud and careless behaviour, said nothing out-of-place and stayed by Natsume's side the whole timenote In one scene, Nyanko-sensei examined Natsume's childhood drawings behind the wardrobe by himself with silent interest, showing just how much the he had come to care for the boy.. Despite all the years past, Natsume still could not help but break down in tears at having remembered everything. With his purpose fulfilled, Natsume leaves the house for the last time with a final "I'm going now, dad", bringing a beautiful conclusion to his arduous homecoming. Also double as a massive Tear Jerker.
Chapter 26, where do we start? When Nishimura and Kitamoto visit Natsume so Nishimura can offer to take Natsume's place in the bazaar because he was worried Natsume was feeling uncomfortable and just wasn't speaking up. Then Natsume's flashback of Nishimura and Kitamoto teaching him how to ride a bike. Then finally near the end, Nishimura and Kitamoto coming to check on Natsume and giving him a scolding (out of concern) for being so careless, telling him that they can tell them anything.
The first OVA, in which Nyanko-sensei protects and guides a pair of children who are wandering through a forest.
Especially the times when they suddenly disappear and are randomly climbing trees at a 45 degree angle over a conveniently-placed precipice, and Nyanko panics before rushing in like every animal babysitter in cartoons. Let's face it, Nyanko-sensei is a Friend to All Children even if he would never admit it.