Bob saving an innocent binome from deletion, at the last second, in "Racing The Clock."
All the effort that not just Dot but effectively all of Mainframe go to in order to assemble Enzo's birthday, which, based on the audience, seems to be on the level of the largest social event in Mainframe.
Bob and Enzo's big brother-little brother relationship is heartwarming. Enzo idolizes Bob for being Mainframe's hero, while this one acts as a cool Big Brother Mentor to Enzo and often takes him to do racing and other sports together during his free time, in addition to mentoring him during games. And despite Enzo's brattiness and annoyingness at the beginning of the series, Bob never shows any annoyance toward him, instead keeping his charming, upbeat and friendly attitude all the time.
Enzo: Uh, Bob? Thanks again for spending all this time with me. Doing all this stuff with you is the coolest present I could ever access!
Bob: Don't mention it, Enzo, it's your first birthday. You deserve to be spoiled! Now go on, I'll be right up.
AndrAIa's introductory (eponymous) episode combines this with a Moment of Awesome. In the middle of the underwater game she originated in, she manages mid-game to strike up a friendship with Enzo, but in the middle of a skirmish toward the goal, Enzo is horrified to realize she's a game sprite, and his new friend will inevitably leave with the game (amplifying Enzo's frustration earlier in the episode of feeling desperately lonely with no sprites like him around the city). AndrAIa ain't going out like that, and unleashes an awesome Indy Ploy - after knocking out Enzo, she downloads a backup of herself onto Enzo's icon, locks Enzo up in a torpedo and launches it toward the goal, thus beating the User, winning the game, and saving Bob, Dot, and Enzo from being nullified. Moments later, back in Mainframe, Enzo's icon is pressed and AndrAIa materializes, becoming the first known game sprite to show up outside of a game. Her first act? Hugging Enzo.The screen may get a little blurry by this point.
This one might have an element of Fridge Horror to it - what if that backup means that this AndrAIa is a copy of the original, who's still hopping around the Net with the original game? Or it really did back up her data on her Icon before it released her thinking she was Enzo, as she said - but either way, what AndrAIa did was incredibly sweet and the end result is no less heartwarming.
A small moment comes towards the end of "Painted Windows". As Hex lies on the floor in the fetal position, weakened and shaking and practically catatonic, Scuzzy immediately rushes to her side in concern, and Bob leaves Mike the TV behind to keep her company and help her get through it. By "Nullzilla" the two of them are shown to be getting along surprisingly well.
In "Web World Wars", we see the culmination of Bob and Enzo's relationship. Deciding that Enzo had earned becoming a Guardian like him, Bob downloads the Guardian code to his PID and, despite knowing full well that Dot wouldn't approve, appoints him his replacement as Mainframe's defender if something happens to him (Bob).
Enzo: Thanks, Bob!
Bob: No, Enzo, you've really earned this. You will be transferred to the Supercomputer to attend the Academy and become a full-fledged Guardian like me. I know you'll make me proud.
Dot being reuinited with Cecil (whom she had presumed deleted) at the end of "To Mend and Defend".
When AndrAIa is near-fatally injured by a Web-Creature, Princess Bula suggests to Matrix that an energy transfusion might buy her some more time, but warns him that it "might hurt". His response?
Matrix: Do you think I care? Throw the switch!
Matrix has to be called away from the energy transfusion he's giving AndrAIa because the ship's under attack. At the end of the episode, Mr. Christopher stumbles upstairs and we find out he'd taken it upon himself to donate energy to her during the battle. This is the same character who complained earlier in the episode about not turning a profit.
When Matrix and the gang finally, finally find Bob in the Web, mid-season 3. And Bob even saves AndrAIa's life for good measure. And just to cap it off, Matrix' reaction is to instinctively yell "BOB!" and nearly perform a glomp like he did when he was a Bratty Half-Pint. Even after everything Matrix has been through, he's still little Enzo deep down, and wants to be close to his hero.
Bob: WHOA! I think you're a little too big for that!
Captain Capacitor's kindness in helping Matrix search for Bob in the web. At one point his crew even questions what they have to gain from it and he only responds that helping Matrix is his way of repaying Dot and in doing so is more important than any valuable.
An easily missed one due to the lighting, but in "End Prog," Mouse retrieves a binome girl's guardian teddy bear. Heartwarming enough in itself, that she pauses in the middle of the system's likely deletion to give her this little comfort, but this is the same style guardian teddy bear that we've seen Mainframers with since the show started - but it's GREEN. As in it's not in the image of Bob, but Enzo. Particularly heartwarming considering all the difficulty he had to go through to gain that acceptance, given that everything about him, from age to the fact that he's green instead of blue, was originally criticized.
In "End Prog" Ray offers to take Mouse away from the system but Mouse refuses. When she suggests for Ray to leave if he wants, he refuses as well.
Glitch, the Keytool, had one when it offered to merge with Bob when the Saucy Mare faced an impossible situation - unless they lowered the shielding they'd assembled of dead Web creatures, Mouse's countermeasures would destroy them in their programing to keep out said Web creatures, but the shields were in place to prevent the crew from degrading in the hostile environment of the Web. It seems they're stuck on the outside of Mainframe looking in, when Glitch abruptly begins to emit Keytool Speech and offers to merge with Bob. Bob makes it clear that it's something of a Heroic Sacrifice, indicating that Glitch wouldn't retain at least its own individual consciousness, but Glitch is on board with getting them all home.
Bob de-fragmenting Hex's mask in "Showdown."
There's also her agreeing to send Bob to rejoin the others.
Hexadecimal: For you, Bob... anything.
Note that he never seems anything but concerned (either for Mainframe or Hexadecimal) during this scene. He genuinely wants to help her, its not just an escape ploy. This is actually Fridge Brilliance, since in the following Season we find out that Bob was always interested in reforming viruses rather than deleting them (which was considered a radical view among Guardians). Makes perfect sense for him to be interested in helping her, even if the same logic ultimately doesn't work at all for Megabyte.
Matrix and Dot reuniting doubles as a Tear Jerker, in a Tears of Joy sort of way. He has the most adorable smile and her tears as she realizes her baby brother is safe and back home are just so heartwarming.
Hack and Slash comforting each other during "System Crash" and "End Prog".
Dot and Hexadecimal searching for the Null that was Wellman Matrix so that Hex can restore his sapience. She fails at first, but when Dot begs her, she realizes that Wellman is in some sense her father as well and tells Dot, "I'll try again, Sis." Extra heartwarming as Dot and Hex are also romantic rivals and were enemies not long ago, yet Dot trusts Hex and Hex will do her best to make Dot happy.
Of course, once you remember that she referred to her and Megabyte always trying to kill each other as just sibling rivalry...
Hex's complete acceptance of how countering Daemon's infection of the Net will require her to commit a Heroic Sacrifice.
Hexadecimal: What's the problem? We've got a Virus, me! Give me the cure and I'll fix everything.
Bob: Hex, you won't survive this. It's a one-way trip. Total fragmentation.
Hexadecimal: But you will survive.
And then her final words to the others.
Hexadecimal: Bob, I have always loved you. Dot, look after him and... be happy.
Say what you will about the restoration of Bob from his Web-damaged state back to his classic appearance, you can't fault Glitch's motivation - allowing his friend and companion to be whole again after Megabyte took some of Bob's code.
AndrAIa might be infected by Daemon at the time, but in her casual girl talk with the supervirus, she reveals that she knew from the start that Enzo wasn't a Guardian like he claimed, that he was just trying to impress her. Reframes her referring to him as 'Guardian' while they're kids into her trying to encourage him to live up to that ideal.
After Matrix and "Bob" beat Pantsu Hebi X, they celebrate like when Matrix was a kid. "Bob" accidentally calls him Enzo and promptly apologizes, but Matrix likes how it reminisces him of their original friendship and tells him that he's doesn't mind being called that by him. Granted, it's somewhat offset by the fact that this "Bob" is actually Megabyte. But still, it's heartwarming that Matrix would allow who he thinks is Bob to call him that when he doesn't let anyone else, not even AndrAIa.
Matrix praising Little Enzo for helping them win a game. "That was okay, kid" may not sound like much, but judging from Enzo's response, and AndrAIa's comment ("High praise indeed!"), it was high praise coming from him.