Perhaps the show's concept itself, two friends playing video games together and the internet having a good time watching them have a good time.
In the 20th episode of Pokemon Emerald, Jon takes a picture of him and Ego relaxing on the couch. As they're talking about sharing it over twitter, it pops up on screen. The picture looks exactly like a picture you'd find on anyone's Facebook or Twitter: Two Gamers on a Couch, hanging out and smiling.
In the Aladdin finale, Jon and Arin can't stop talking about how beautiful the carpet ride bonus stage is, even singing along with "A Whole New World". It's actually kind of sweet.
In Kirby's Return to Dream Land Episode 2:
Jon: Is that Arin and Jon agreeing on something? What is that shit?
Ego: It's really strange how often we disagree.
Jon: Yeah, but it's funny. I remember when we were first starting Game Grumps, cos I was like worried, I was like "Do you think we're ever gonna like fight or y'know disagree" and it was like "Naw. We argue a lot, but it doesn't affect our friendship." And I was like "Yeah, I guess you're right." We argue SO MUCH and it's always like "Awesome! I'm glad you feel that way. Come over next time?"
Near the end of Super Mario Land:
Jon: You've never once lied to me in my life.
Ego: *sigh* I did. I did once. When I said I hated you.
It is just kind of heartwarming seeing that despite how young the project really is, the fanbase for the Game Grumps is strong and wonderful (with the large amounts of cool remixes, animations, etc.) to the point where Grumps and fans alike call it "the best fanbase ever".
The finale to Kirby Super Star was pretty nice, with Jon talking about how they just finished their first game, how far they've come with Game Grumps, how great the fans are, and how it's really made the two of them best friends.
During part 2 of Wild Guns, Jon comments that he hasn't seen Arin have this much fun playing a game in a while. Considering whatgames they have been playing lately, this might not be too far from the truth.
At one point during their Magfest panel, one fan wanted to ask Barry a question. Jon took out his phone and called up Barry, and when Barry answered, Jon just said, "Hey man, you're live at the Game Grumps panel!" and the crowd went NUTS! A massive cheer was sent up and there was a "BARRY! BARRY! BARRY!" chant. When the noise died down, Jon asked if Barry was still there, to which he responded with a choked up, bordering on Tears of Joy "Yeah!"
Also, there's Jon berating Arin when he was clarifying that Jon went to get him Powerade because he was too sick to do it himself.
Jon: I'm gonna pause this... Are you fucking implying that you w- of COURSE you were too sick to get it!It's not like you were being a douchebag, what? I would've asked you for fucking SEVEN Powerades!!!
Any time Jon squees over something in a game. While both of the Grumps love games with all their heart and souls, whenever Jon encounters a good one (or at least one with something he enjoys) his happiness comes across completely. One of the best examples of this is the first episode of Kirby's Return to Dreamland where Jon (and Arin) is barely able to contain his joy to play what he considers an excellent addition to an already excellent series.
Jon: "Do you just see a girl you wanna marry, because I'm worried for you if you're walking around being all like, 'I wanna marry her!'"
Arin: "No, not in public, in my house! Because she lives with me."
Jon: "[giggling] Awww, that's even cuter, stop it!"
From another Sonic episode...
Arin: I don't really care anyway I was just filling time.
Jon: BAPADABOOP BOOP BEEP- What do you mean 'filling time'? I'm not good enough to be time alone? I-I can't be your time? You have to fill the time with me?
Arin: Uh yeah...I have a good time when I'm with you.
Jon: *Laughs happily.*
From Sonic '06, Jon actually having fun as Blaze. He even compliments her, saying she's cute and reminds him of Dot.
From yet another Sonic '06 episode (75 to be precise): Jon storms out of the room while Arin makes noises, and "fires" Barry. But when he's coming back, Jon is apparently asked by Barry if he was serious, and the mic picked up his reply. It's a silly moment but sweet at the same time.
Also the way Jon asks Barry to add that extra scene in at the end of the video is also pretty heartwarming.
Near the end of Mario Party 2 Revengeance Part 6, Arin makes a joke about calling a "Side-kick rental" service and asking to refund Jon and replace him. When Jon tells him that he heard the whole thing, Arin says he was talking to his karate instructor, who taught him how to "side kick". By the end, after a high five, Jon says something about hurting the ones you love without realizing, to which Arin responds by calling side-kick rental back up to say he didn't mean what he said. Jon still gets upset at him for lying though.
In Sonic 06 part 78, Jon gets a call from his mother, who he puts on speakerphone for the audience. She called him to tell him his father survived a dentist operation, and acted really shy when told she was on the show. The entire exchange is filled with adorable. In a bit of Meta-heartwarming, the fans seem to have taken a liking to her, calling her MomTron.
The entire Grant Kirkhope episode is one. You can tell Jon is in awe of being in the presence of one of his idols.
In Sonic 06 part 85, after getting their sweet revenge on Sonic as Silver (Complete with evil laughing from Arin) they agree that the whole channel was worth it because of the friendship they've forged through it.
The epiphany in Donkey Kong Country 2, part 6. It's interrupted by an in-game death and the two proceed to joke about humiliating themselves for others' enjoyment, but what Jon said was completely sincere.
Jon: "You know what's the compliment that we get about our, like, fanmail or whatever that makes me the happiest every time I see it?"
Arin: "What's that?"
Jon: "It's when people are like: "Fuckin... Whenever my day sucks, I watch Game Grumps and it's better." And I'm like... There is a reason to do this."
During Magfest, Jon and Arin try to recall how they became such good friends. Their first meeting is described as Arin answering the door with a plate of cookies and Jon standing outside with a pack of Dr Pepper. It is a sweet moment.
Jon's heartfelt thanks and appreciation towards the show's viewers in his retirement announcement.
Any moment, especially in Super Mario Bros. 2, Mega Man 2 or Jackal, where Dan makes Arin burst into uncontrollable laughter. While it's sad that Jon left the show, it's clear that Arin and Dan's friendship is just as strong.
The fanimator GregzillaGT made an animation that was intended as a brief tribute to the end of Jon's run on the show. After going through some of his funny moments, the final scene shows Jon leaving on a gigantic Jacques, the others looking on sadly (Arin especially). The very end has Jon outstretching a hand so Arin can high-five it right before leaving, all set to a melancholy orchestral remix of "Pause Balls".
During The Legend of Zelda run, Danny takes a moment to ask Arin if he's got any messages along the lines of "Game Grumps saved my life". He confirms that not only have they got messages like that, they've got messages about how people have got into relationships through being fans of the show and wearing the merchandise in public, causing someone else to recognise it and strike up a conversation...
Also during The Legend of Zelda run, Dan tells a few stories involving his dad. The only one where he doesn't do an impression of him with a silly accent is when he talks about when his dad quit smoking.
Arin's story afterwards recounts his friend from when he worked at Blockbuster who had been a heavy smoker until she found out she was pregnant.
So far, most of their Kirby's Epic Yarn playthrough consists of Arin and Danny acting extremely cheerful and squeeing at everything in sight. They claim that it's impossible to be grumpy when they're playing it.
In Part 4 of the Super Castlevania IV playthrough, Suzy stops by to give Danny some tea, at first the Grumps are all hammy and then sincerely appreciate Suzy stopping by.
In Part 9 of Kirby's Epic Yarn, Danny recounts a story about his grandparents' wildly differing opinions on coarse language, but then mentions how they were together for 62 years. He then comments Arin and Suzy are the same, to which Arin says 'I hope so.'
Their project of selling their game copies on Ebay sent to the Grumps raised 7,000 dollars towards Childs Play. Their appreciation for the fans is truly heartwarming.
The inclusion of Barry and Suzy when doing multiplayer games with at least four people on Steam Rolled makes it feel like they're all one big family.
Speaking of Suzy, her character is Suzy the Outlaw. Aww, she's a criminal just like her husband, Arin the Bandit.
F.L.U.D.D.'s apparent death during the Super Mario Sunshine finale leaves the two appropriately shocked as they believe it to be the end. After which they are appropriately relieved at the sight of it still being functional.
In one episode of Super Mario Bros. 3 Danny and Arin talk about the uncomfortable factor of becoming well known that it can be risky because it becomes harder to tell who is being nice and who just wants something from them. Arin admits he doesn't have that problem, it sort of helps his confidence but he knows Suzy loves him since she was talking to him before he became Egoraptor. Suzy loves Arin Hanson the artist not Egoraptor the Awesome series guy.
The Amazing Frog? one-off is both funny and this during the fight over the crown at the end. Arin and Danny are having so much fun just dicking around that it spreads to the viewer, who is likely laughing as hard as they are.
A real life example, but as of October 25th, 2013, Arin and Suzy finally married.
There's quite a bit of sadness involved by for the first time ever Danny tells the story of his depression, learning he has OCD and over coming it. It can be found here. The entire episode is worth watching. Arin is incredibly supportive of Danny.
That's not even discussing the fact that Danny discusses it because of all of the people willing to share their stories with the Game Grumps about their own struggles. He felt like he needed to pay it back to them.
Part 26 follows up on this at the very end, as Dan thanks everyone for their support and letters and stuff (and reminds them not to throw away their meds like he did, and to actually talk to a doctor about getting off them).
And on the less heavy side is that Arin and Danny both hate the term 'aspiring artist' and declare that if you write/draw/paint/create music ect. then published or put out or whatever then you're already an artist.
Part 29 of the Kirby's Epic Yarn playthrough. Dan brings up his Bar Mitzvah in Israel and how proud of himself he felt after getting through it. Also it was one of the few times he and his Israeli grandfather were particularly close, due to the living distance between the two of them.
The Epic Yarn finale reaffirms just how damn happy and adorable the game is. Danny can barely contain himself at the end.