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.
While their tangent on gay marriage was rather comedic, the fact that Jon and Arin believe in allowing gay marriage and their surprise at how it's still not universal in America was very sweet.
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!"
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.