"Hey, show up with an army of undead warriors to save the day, and suddenly you're everybody's best friend." Nico finally feeling accepted.
"And it was pretty much the best underwater kiss of all time." Certainly heartwarming for the Percy/Annabeth fans, but think about this: Percy has finally earned his reward after four years of absolute torture.
Poseidon telling Percy that he was his favourite son.
Ditto for Percy getting a hug from his dad for the first time at the end of The Last Olympian.
Tyson talking about how alone he felt on the streets, and even praying to the gods yielded no results. Then the gods sent him Percy.
The reveal that the bits of metal Tyson had been tinkering with for all of book 2 was a special shield for Percy.
A shield that ended up saving Percy's life in the next book, at that.
In a Fridge moment, the Bookends moment near the end. Percy holds his shield over Thalia in an attempt to protect her from the Manticore; at Mount Orthrys, she pays him back by using Aegis to shield him from the force of the exploding car.
Hades being all stunned at the warm welcome he receives from the other Olympians at the end of book five.
Calypso letting Percy go. The fact that she loved him enough to let him go, even though she'd spend thousands of years waiting for a new love which would be ripped away again anyways... Also doubles as a major Tearjerker.
Annabeth taking the knife for Percy in The Last Olympian, and then that entire scene where Percy tells her about his Achilles spot.
Zoe Nightshade sacrificing herself for Artemis. Even though Artemis was a goddess and couldn't really be killed, Zoe didn't even hesitate before throwing herself between Atlas and her lady. Artemis' clear anguish at her lieutenant's death, coupled with the fact that she chose to give her the highest honor imaginable, preserving her spirit in the stars, adds to the tear-jerking legacy Zoe left behind.
And while we're on Zoe, the fact that she sobs—literally breaks down and sobs—after Bianca's death is not to be shrugged off. This girl is over two thousand years old, has had more than her fair share of loss, and has known Bianca for less than a week. But she is a Hunter, and she trusted Zoe to protect her. And Zoe couldn't, and she mourns her loss as if she'd known her a thousand years.
Zoe's entire relationship with Artemis is this, whether you read it as simple loyalty or something more. She was willing to take the entire weight of the sky to rescue her goddess... and Artemis knew it, and wouldn't let her. She didn't even get a chance to open her mouth before Artemis cut her off.
"No! Do not offer, Zoe! I forbid you."
In The Last Olympian, a very subtle CMOH is when Percy and Annabeth, riding through the city, in the middle of a huge battle to save the world, stop to help people who have fallen asleep in dangerous places, like in front of cars, and put out fires. The end of the world is going on, and they still care enough to stop and make sure people are safe. Because they're heroes, and that's what heroes do.
Percy breaking the cycle of half-blood arrogance, after learning what Hercules did to Zoe: "If I'm going to survive, it won't be because I've got a lion-skin cloak. I'm not Hercules."
And later on, Zoe acknowledging the truth of the statement. "You spoke the truth, Percy Jackson. You are nothing like... like Hercules. I am honored that you carry this sword."
Even more heartwarming when you consider that she gave Riptide to Hercules because she thought he was a true hero, brave and strong and noble, and that she was starting to love him. Percy is all of that and more, and it's clear that Zoe does care for him—almost as a brother—after everything they went through together.
To be completely honest, Percy’s relationship with his mother is completely this. There is nothing they don’t share and nothing they won’t to for each other
Percy's relationship with his new stepfather Paul and Sally's relationship with him as well could also be seen as this; especially after years of putting up with Smelly Gabe
Paul asking for Percy's approval to marry Sally, because he thinks that Percy has a right to know, before he asks.
Especially in the Last Olympian when Paul says that he wishes he had Percy's courage to do something incredibly dangerous that could save them all. Percy even says that he doesn't get compliments like that a lot.
At the end of the fifth book, after the gods are finished rewarding everyone, the cyclopes form an isle while standing at attention, and before Percy leaves Tyson says this.