That scene in #33 where Ax teaches Tobias about Andalites. D'awwwww. Finishing up with him teaching Tobias the words to the evening ritual. "From the rising of the sun to its setting, we place what is hard to endure with what is sweet to remember, and find peace." Pretty much sums up the whole rest of that book, in a very Tear Jerker way.
Cassie holding Ax's hand at the end of #38, while he cries.
The same book, when Ax wakes Tobias with the question, "Are you my friend?" and Tobias replies, "Ax, we are the two strangest creatures on this planet: a freaky, four-eyed, half-deer, half-scorpion, centaur-looking alien, and a bird with the mind of a person. We've fought side by side. We've been nearly killed several times. Of course I'm your friend."
Especially moving because the thing that really gets Ax is the "of course."
In the same book, Ax says in the narration that he thinks of Tobias as his shorm. Shorm is the Andalite term for best friend. The word shorm literally means "tail blade", the expression being that a shorm is someone who you would trust to hold their tail blade to your throat.
Especially touching because while Tobias knows that since he is Elfangor's son that Ax is his uncle Ax is completely unaware of that but feels the same familial connection towards him.
How about Tobias being reunited with the mother he never knew. The heartwarming is taken up a notch when she gets the power to morph and regains her vision.
Aftran after giving up so much for the Yeerk Freedom Movement is allowed to become a whale nothlit and live a full life in the ocean. Awwww.
Marco's parents finally being reunited after years apart.
Alloran, temporarily abandoned by Visser Three and knowing that Ax won't kill him, begging Ax to get word to his family that he still loves them. Even after learning about some of the terrible things he did... it's a reminder that he's still had his life stolen away.
Alloran moving his tail of his own free will and yelling, "I did! I did it!"
The scene where Marco realizes that although it might be smart to let his father become a controller, he still can't go through with it. "This was the end of smart, and the beginning of right."
The story of Essam and Edriss, and their infiltration of Earth. Over the years, both became influenced by their human hosts. Edriss (Visser One) even came to call her own host (Allison) something akin to a friend. Allison tempted Edriss with human emotion and feeling, and it created very human feelings within the Yeerk. And the two hosts, with the Yeerks, fell in love and had children together. At the very end, when Edriss wanted to return to the Yeerk Empire, Essam refused. He had become so much like a human that he had, in some ways, become human, entering into an effective symbiosis with his host. He was unwilling to surrender that humanity even at the cost of his own life, in order to protect the children. And Edriss, Visser One? Throughout all her invasion of Earth, one of the primary reasons that she railed against the very idea of an all-out war wasn't because it wouldn't work (though she didn't think it would). It was because she could not, would not allow her twin children to potentially be hurt.
And beyond even that, she learned and kept the secret of the "Andalite bandits" from Visser Three, despite all the damage they had done to the Yeerks. Partly because it opposed the other Visser. But also partly because if their identities were exposed, then it might threaten the children she had in her previous host. Edriss came close to allowing herself to die in order to avoid hurting one of her children (and was saved from that very situation by a timely interruption by the Animorphs). She was probably more human than Yeerk in the end even by her own admission, and even after she returned to the Yeerk Empire. More a human influenced by Yeerk ambition and desire to rule than anything else. And when Essam took her children from her, she didn't go after him for revenge. She went because she wanted her children back and because even then she thought of him as her friend. So much of what she did was coloured by the humanity she had unknowingly assumed. That humanity could so influence even a Yeerk (and the highest-ranking Yeerk beyond their ruling Council of Thirteen, at that) is, to this troper, a Heartwarming moment.
When Visser One calls Marco for help while on trial in the Yeerk Pool, she tries to manipulate him by telling him what his mother is feeling. It doesn't work, but his response is still pretty moving - especially because of how proud Eva is of him afterwards:
Marco: Mom, I know you're in there, and I know you can hear me. I don't know if I'm going to be able to save you. You understand that, don't you? I have to do what's right.
Visser One: Your mother loves you, Marco.
Marco:(very angrily) I know my mother loves me. And make no mistake, Yeerk, there isn't any peace between us. One day, soon, I'll kill you for what you've done to my family. (Phone slam).
During The Ellimist Chronicles, we finally get a good look at the war between Crayak and the Ellimist. Before they became gods, anyway. Crayak ran around space, creating games and using the Sadistic Choice against the Ellimist as much as possible. The Ellimist rarely won, and even when he did, people still died. Eventually he gave up and settled on a distant planet, where the Andalites were still at pre-stone age technology levels. There he was reminded of the simple truth that every living species knows instinctively: If you can't stop the thing killing your children, compensate by making more children. He returns to the stars, seeding every world he comes across with primitive life, which means no radio or Z-space signals to attract Crayak. Then he created the Pemalites.
The Ellimist: To the Pemalites I gave technology. They became an advanced species within a few decades of my creating them. As their creator, I gave them laws: They would never practice violence, and they would conceal their existence as long as possible. And I gave them a mission: to carry life everywhere.
Jake and Cassie's firstkiss in The Attack, considering he previously believed her to have died.
The Departure, partly because of quotes like this:
Cassie: No, I don't think we can make peace between all humans and all Yeerks and all Andalites. But you and I can have peace. One Yeerk, one human.