The Arbiter and Half-Jaw (the Spec Ops Elite commander) did not start off the right foot, but even when the latter became suspicious and distrustful of the Hierarchs' decision to replace the Elites with the Brutes as the new Honor Guards, he still trusted the Arbiter implicitly after the events of the Gas Mine at Threshold. It was that trust that united most of the Sangheili under the Swords of Sanghelios by Halo 5: Guardians.
Halo 2 Anniversary
In the opening Terminal scene with Locke and the Arbiter, the Arbiter tells Locke that while he and the Chief were once enemies, the Arbiter now considers him to be a friend.
At the start, when they think the Chief's dead or incapacitated, Johnson wants heavy lift equipment, because "We're not leaving him here." And then the Chief's hand grabs him, and he speaks up, and Johnson gets cheerful. Less gloomy. Whatever. Point is, it's a great demonstration of camaraderie.
The Master Chief and the Arbiter start off as enemies briefly, but eventually trust each other after several skirmishes. While the Chief doesn't say more than only one word to the Arbiter, it is clear that he trusts him implicitly, such as when he allowed him to kill Truth on the Ark, and when they became back-to-back against the Flood. They've come a long way since they met in the bowels of Delta Halo.
Cortana the level, when you reach Cortana the person.
Cortana: "You...keep it. I do know how to pick 'em."
John-117: "Lucky me."
As if that wasn't wonderful enough, keeping in mind the background from the Fall of Reach novel makes it even better.
Also, this Call-Back right after you've retrieved Cortana, mirroring the start of the first game, delivered in the most heartwarming way by Jen Taylor:
Cortana: "Just keep your head down... There's two of us in here now, remember."
The departure of the Sangheili at the end.
Rtas 'Vadum: Things look different, without the Prophets' lies clouding my vision. I would like to see our own world. To know that it is safe.
Arbiter: Fear not. For we have made it so.
Mendicant Bias was a forerunner AI that defected to the flood. He was captured and split in two: One part on the Arc, one in High Charity. What makes this heartwarming? When the Covenant opened the portal, the two parts of Bias reunited. Filled with regret, knowing he was dying, he decided to betray the Flood, and protect John from the dangers of the Arc. Particularily heartwarming is this message to John, found in one of the terminals.
Mendicant Bias: And so here at the end of my life, I do once again betray a former master. The path ahead is fraught with peril. But I will do all I can to keep it stable - keep you safe. I'm not so foolish to think this will absolve me of my sins. One life hardly balances billions. But I would have my masters know that I have changed. And you shall be my example.
At the credits of Halo: Reach, Bungie gives a goodbye letter to its fans. No true Halo fan could read it without breaking into tears.
At the end of Halo: Reach, we see Reach...in 2589. The grass is green. Snow sits on the mountains. And Noble Six's helmet still lies where it fell, and Dr. Halsey's voice speaks over the peaceful vista, telling you that your death was not in vain, and that through your courage, humanity was ultimately able to survive and rebuild.
When Vergil/Quick approaches Dare in the data centre, Dare removes the last explosive harness from its side and pats the Engineer softly. Dare's also noticeably gentle when instructing it to stay behind her. Its probably the first time in a long time that Quick has ever been treated with such care and respect, and its pretty obvious he enjoyed it.
When one considers the Engineers are clearly abused in the Covenant, its kinda obvious that Quick to Adjust is pretty happy to be leaving in the care of people who would treat him properly. Even when in interrogation they still let Vergil tinker with tech, albeit under supervision.
In the final audio log, the surviving refugees quickly board the train, but ensure that everyone is on board, some helping others onto the train. And they take the time to wait for Sadie and Branley to join them.
Jonas, the kebab merchant in Sadie's Story. Rather than choosing to flee like all the other civillians, he stays. Partly because his obesity renders him incapable of running, but mostly to give away kebabs for the fleeing refugees. Guy's a damn saint.
Pretty much every scene Master Chief interacts with Cortana is this. Especially when she finally manages to touch him, right before she dies.
When John learns that Cortana is suffering from rampanacy, the Master Chief's immediate reaction is that if he can get her to Catherine Halsey, she'll be able to repair Cortana. It's heartwarming because despite the backdraft Halsey has been receiving from Halo canon over the last few years, the scene is a stark reminder that John will never lose faith in her.
More than just lose faith in her, it smacks of "we'll take you to mommy, mommy will make you all better". Long awaited acknowledgement in the games what was established in the books: the Spartans think of Halsey as their mother.
The Chief's refusal to even consider the possibility that Cortana might succumb to rampancy. Rampancy is an inevitability for AIs, yet John keeps insisting that he will save for. After a while, you starting thinking that maybe, just maybe, he will defy the odds again and save the day.
The Forerunner Saga
Humans and Forerunners finally come together on friendly terms following the Halos firing. They both attend a ceremony and mourn and even dance together. Trial, a Lifeworker overseeing humanity, has this exchange with Riser:
Trial: "You know, humans and Forerunners were always meant to be brothers, not to fight like we did."
Riser: "Brothers fight too, you know."
Then, when humans are brought to earth, Riser and Bornstellar share some parting words:
Bornstellar: *In regards to the Portal on earth* "Perhaps one day your children will make their way back, and I hope meet our children"
Riser: "I doubt even I will live long enough to see that day. But it is good to think that one day our young will rise to another challenge as brothers should: making trouble, finding strength."
Bornstellar: *Overcome* "Hope..."
Halo 5: Guardians
"It took you long enough."
—Catherine Halseyupon being reunited with John-117
The rapport between members of Team Osiris and Blue Team are heartwarming in separate ways. Team Osiris are a Band of Brothers, while Blue Team is a Family of Choice. Watch the ways they interact. Osiris have a confident yet warm bravado, while Team Blue are more subdued and caring towards each other.
When Cortana and Blue Team finally meet face-to-face, Cortana begins to walk towards Chief, and Linda silently moves in front of him as a shield. The moment is doubled when Chief gently moves her aside, proving that, even after all she's done, even after she's become an insane dictator and bullying megalomaniac, Chief still trusts Cortana.
Halsey begged Locke to bring John back to her. In the ending, the SPARTANs return, and when Halsey comes forth, Locke is there - with John beside him. All wishes fulfilled.
When the Arbiter speaks with the Spartans in Sunaion, he asks Locke to "send [his] greetings" to the Chief. After Halo 3, it is endearing to hear him still consider Spartan-II a friend. It's also heartwarming of how friendly a Sangheili is to a human.