In Wii Party during Globe Trot, near the end, Max completely stops trying to win, just so Peter can win, to the point of outright avoiding one Hot Spot that would've won him the game so that Peter could have a chance of getting it. Unfortunately, it didn't work, since one of the computers got the final Hot Spot first.
Also in Wii Party, Peter and Max get 100% in Friend Connection, which they claim to have wanted to get for a long time.
A small example in Welcome to Ponyville; when Max goes to see Trixie's show, he says that he really wants to chew Trixie out. However, when the opportunity presents itself, he hesitates, suddenly not so sure he wants to yell at her. He ends up doing it anyway, though.
The Secret Santa in Hearth's Warming Minecraft, where the guys get each other gifts; Peter and Zero are Trolls, with Peter getting Max a wool dildo and killing him with lava and Zero just blows up a nuke for Peter, but Max gets Fury a golden sword of justice and Fury not only sings Zero a song, but also gets him a musket with ammo. Then, at the end, the guys take a picture (screenshot) of them in front of a tree they planted in the crater made by Zero's nuke present for Peter.
In a Tumblr post, Max decides to give an explanation for his suddenstupidity in Tekkit. During his explanation, he says that he considers Peter to be a Tekkit genius.
In Skyward Sword and Super Vexation Saga, Peter goes on about the Creeper plushie Max got him for Christmas and constantly thanks him for it.
Surgeon Simulator 2013: "I am recording this on Valentine's Day; the heart is all that matters!" Even though this was meant to be a pun, it's still a small example.
His third "What the Hell?" Moment for Left 4 Dead 2 actually has a moment of heartwarming. For pretty much the entire video, both Zero and Alec are making fun of Max or getting annoyed by him. However, at about the 3:10 mark, Alec gets knocked down by a Tank and groans about how he needs to get a medpack as Zero revives him. Max, meanwhile, walks over and takes the medpack Alec said he needed, using the excuse that he (Max) had already died once and needed it more. Not even twenty seconds later, Alec gets caught by a Smoker. Max quickly runs up, shoots the Smoker, and uses the very medpack he just took to heal Alec.
Sonic Spinball of the Super Vexation Saga reveals that Peter got Max a t-shirt with Max's ponysona on it. Max wears it proudly throughout the episode.
Peter being willing to let Max's first try at the game be a practice round, since he hadn't played the game ever before, while Peter is an expert. While some would say this is more "fair" than "heartwarming", none of the games before this had any sort of practice, and Max is usually able to adapt to unfamiliar games rather quickly. So this wasn't so much Peter being fair as it was Peter bending the rules to give Max more of a chance. In the end, though, it didn't help Max win.
In one episode of the Sonic the Hedgehog 2006 race, Max says (jokingly) that if Dan beats Radical Train first try, he'll slit his throat. Dan asks him to please not, because "I actually sort of like you".
We also learn during said race that, as a birthday gift, Max sent Dan a Wii U. (And the copy of Sonic the Hedgehog 2006 that he's using to record.) And in part 9, after jokingly offering a deal to give Dan ten dollars for Hyrule Warriors in exchange for Dan dying in the game, Max says he'll send the money anyway.
Throughout The Walking Dead, Max has consistently chosen the options that let him kill a character, with two "exceptions" - the first time, the character suffered a Fate Worse Than Death due to incoming walkers (and it had been the result of a coin flip anyway), and the second time, it was being pragmatic by not giving someone a Mercy Kill and attracting attention. The first time Max outright subverts this and chooses not to kill a character or let them die, just because? Saving Ben in episode 4. After having clearly disliked him in episode 3, and only just starting to feel more neutral about him this episode.
Adding onto that, Ben willingly joins up with Lee at the end of the episode after Max leaves the choice up to him. Granted, Kenny doesn't join, which kind of ruins it...
And while it crosses with Tear Jerker, the fact that Ben's eventual inevitable death is what finally pushes Max over the Despair Event Horizon is further heartwarming, showing his attachment to Ben.
Max makes two teams of "people who are awesome". These teams consist of worms named Rhino, Enigma, Dan, Zero, Peter, Spark, Jero, and Tim; ironically, all people whom he is Vitriolic Best Buds with.
He also says that there were people he couldn't fit because he only did two matches like that and there were only four worms per team. He mentions people such as David and Wren as being ones he couldn't put on.
In the "Tabletop LP" of Mastermind, the death of Monty Oum is brought up. Both Max and Peter appear mournful of his loss.
Being the huge Fallout fanboy he is, you can just imagine how psyched Max was for the Fallout 4 announcement. How he acts in the "reaction and thoughts" video in response to the trailer is like one big optimistic Squee (even though he has some reservations about getting his hopes too high).
You can also see him hugging a Litwick plushie the whole time. Awwww.
Max got annoyed with people bugging him to make Cutie Mark Laboratories and stop making let's plays, and posted on Twitter some irritated tweets about it. Tim, Dan, and Spark then all replied with their own input.
Tim: Those people who tell Max to quit let's plays is basically telling him to say "fuck you" to playing with us, his friends. Nice job