The Order of the Stick has several Heartwarming Moments (all of which are quite spoiler-y, so if that worries you, don't click!)
Start of Darkness
Eugene Greenhilt, amazingly enough, gets one in Start of Darkness. When Right-Eye gives him the first lead on Xykon he's ever had, he refuses to go after the lich. Why?
Eugene: I'm married now. I have a son, Roy. He's almost 8 years old. Right-Eye: So? It's not like I'm asking you to bring him along. Eugene: So if this assassination thing you're so eager to set up goes south, my son is an orphan and his mother, a widow. Or worse, Xykon finds out about them and kills them too, just for fun. The risk isn't worth the reward anymore.
Subverted in Xykon's first appearance; we first see him as a four year old crying over his dead dog Barky; when his sorcerer powers activate and reanimates Barky, he is completely overjoyed. The subversion comes when the newly zombified Barky eats a bird's brains, which entertains Xykon, cluing the reader into his psychopathic tendencies.
The hug Redcloak gets from his mom when we first see them.
Dorukan and Lirian's final reunion.
Dorukan: It looks as if I am to share your prison forever now...
Roy tells his first adventuring group off, both for killing first and asking questions later and for the way they treat Durkon, whom he concedes is "surly and unpleasant" but doesn't deserve suicide mission after suicide mission. After storming off, Durkon goes after Roy, and Roy assumes Durkon's going to "give [him] a parting shot of all-purpose grumpiness." Instead:
Durkon: [T]hank ye for what ye said back there...In all the years I've been in da human lands, yer tha first I ever saw who'd use 'is head when 'is sword was handy. An' ye saved me life, too. I guess I ne'er met a non-dwarf who gave a flying damn about me either. Have ye ever thought aboot forming yer own team? Cuz if ye do, ye can count me in.
Elan's elation when, for the first time in his life, he's told he was right about something, and is invited to join Roy on his quest. Even Roy's snarky comments as Elan's celebrating don't dim the mood.
Bonus published content within the main storyline
At the end of the book version of Don't Split the Party, Elan welcomes Roy back to the land of the living with a five act rock opera about how much he loves Roy- emphasizing that no matter how much Roy disparages Elan's habits, Elan will always consider him his best friend. Although Roy is clearly annoyed once he finds out how long the play is, he decides to weather the whole thing since Elan spent so much time on it.
Rich's tribute to E. Gary Gygax. Many other writers simply did a single lip-service strip that said one panel of "In Memory", but Rich went out of his way to show his gratitude to Gary Gygax, and it shows, in a speech by Roy that could have been read at Gygax's funeral. His recent tribute to the other half of D&D, Dave Arneson, is up there, too.
Goes to Crowning Moment of Funny when Roy's Archon warns him there are tons of adventurers who were not amused by Tomb of Horrors, the "Orb of Annihilation in the statue's mouth" trap in particular.
The reunion of the Order after a very long time, and all the events that come with it. First, getting Roy back. Then, after having a strained relationship for months, Durkon and Vaarsuvius reconcile in a truly heartwarming way; made all the more impressive in that it's combined with a great deal of character growth for both of them and ends on a horrifyingly ominous note. Finally, Elan chooses honesty over drama. "How are we supposed to get a happy ending if we can't be honest?" And Haley reciprocates.
And later on, Blackwing acting as V's conscience to the point that the next time they fight the Linear Guild... well, Qarr says that if Blackwing kills himself, Qarr will make sure V is kept alive after the battle. Blackwing reasons through this by pointing out that he's really only the elf's conscience right now... and if Qarr's so desperate to get him out of the way, it must be working, and Blackwing reaffirms his duty to be there for Vaarsuvius no matter what. Their relationship has come a long way from "Screw this, mammal! You're on your own!"
The founding of Gobbotopia. After multiple strips emphasizing what a raw deal the goblins have gotten (and even more in Start of Darkness), it's nice to see them getting their own nation-state where they can't be casually killed by any wandering adventurers or overzealous paladins that happen by. And their leadership is focusing on issues like diplomatic recognition and trade relations, so they're clearly planning on long-term international relations and not just conquest. It's basically the culmination of Redcloak's dream, and it's hard not to feel good for the goblins despite the place being built on the ruins of Azure City. Especially when you see a cute little goblin kid in the final panel.
It becomes a Tear Jerker, when you remember what she said just seconds before...
A very silly but cute one. During their search in the desert for Girard's Gate, we see a montage of them looking in various ways. One panel inexplicably shows Elan with his sword drawn, apparently ready to duel a cactus to the death. Next panel is Elan and Haley sleeping together. Elan has needles sticking in him, and Haley has a smile and the flower that was on top of the cactus in her hand. D'AAAWWWW.
Rich's final words on the Kickstarter book reprint project before fulfilling the rewards starts, from update #28:
Any way you want to analyze it, it's surprising. Certainly, I'm still shocked. There have already been media stories about it, and there will be more now that we've ended. And they'll talk about crowdfunding and what this success means to the future of blah blah blah. You know what? Screw that. This is between me and all of you. This is because you guys love the story I'm writing, and I love writing it. We made this thing together, and no one is going to replicate it, not exactly. Oh, sure, these records won't stand forever. Some won't even last a month. But it doesn't matter, because you didn't pledge money to me so I could beat a meaningless record. You pledged your money to me because you believe in me and my silly stick figure comic. And that is not something that is going to be mentioned in those media articles.
The last of the strips that Rich did for Dragon Magazine before it switched to an all-web format has one too. After the party breaks the dragon out and saves it from being turned into electricity, we get this exchange:
Dragon: Yes! The sweet taste of freedom! Thank you! Roy: Eh, don't thank us, we just provided a largely symbolic gesture that doesn't actually change anything. Haley: Yeah, we should be thanking you. Dragon: For what? Haley: Everything.
Elan's relationship with Roy is beyond heartwarming, culminating in an Imagine Spot in which his father Tarquin, says that he will adopt Roy, and that he and Elan are now "for real" brothers (and they both get puppies). It's silly, but the cheerfulness of the whole thing is really cute.
Tarquin finally gets tired of Malack's whining about his dead children, and tells him to suck it up. He does, but later, Tarquin showboats around in order to test Elan's skills—something that is very much a tactical liability. Malack yells at him, telling him he's not going to put Tarquin's family over his own, Sabine gets ready to watch them fight... and Tarquin genuinely apologizes for his actions. Yes, they're evil, but they're still friends.
Even The Linear Guild gets its Heartwarming moments. In #804 Qarr makes not-so-veiled threats against Sabine for being loyal to Nale and not The Directors, who are her bosses. When Nale returns after Qarr leaves, Sabine makes her Undying Loyalty plain:
Nale: C'mon, babe. Elan ran this way. If we can catch him, we can turn this thing around.
Penelope's story, overlaps with Tear Jerker, but it's very touching. As a girl, she was caught in a whirlwind romance with an illusionist, a relationship that made a baby girl. The father (Orrin Draketooth) skipped town with the baby. For twenty years, Penelope never stopped trying to find her little girl, even hiring Zz'dtri to divine the location. She would have succeded were it not for V's Familicide spell.
This exchange when between Malack and Durkon, after Malack attacks Durkon.
Durkon: Surrender, Malack.
Malack: So you can destroy me?
Durkon: So I can resurrect ye.
When confronted with the prospect of finding a vampire and killing him on his own, Durkon realizes Thor can't and won't help him and puts his faith in the man he respects the most.
Durkon: What would Roy do?
Even though he's the one who killed Durkon, Malack still puts Durkon's body in a respectful pose, with his hands crossed over his holy symbol. Though this may be diminished somewhat by the vampirification of said body that happens almost immediately after.
He also honors Durkon's last wish, in a way, by letting Belkar live and telling him to get the rest of the Order out of there.
Even after realizing that The Order is still in the pyramid, he chooses to continue honoring that wish by not calling attention to them when they are hiding near where he is passing by.
Also, Belkar trying to rush off and tell Roy about what just happened even though most of his blood has been drained, and he's too weak to stand. So instead he starts crawling.
And his reaction to Durkon dying and being raised as a vampire after Hold Person wears off. He's freaking the fuck out about it.
In its own way, Belkar telling Roy what happened qualifies for this trope, since it's clear he takes it entirely seriously.
"How could this possibly be a joke? Where's the punchline? (...) But trust me, there's nothing funny about it. He just walked in there and saved my life and got straight up murdered for it."
Strip #887. Even knowing it's All Just a Dream, it is full of heartwarming moments, such as Durkon being resurrected, Elan and Nale making peace while their father looks happily, Roy's dad finally entering heaven, Elan being with Haley and Roy with Celia....
Strip #888, "Dream Wedding", somehow manages to be this, Tear Jerker, and a Funny Moment all at the same time. Elan just really wants his family to be happy together. That even includes Nale and the rest of the Linear Guild.
The exact moment crossing over into both funny and heartwarming is the panel revealing that Tarquin is the one getting married and not Elan. It makes the fact that he was comforting Elan for three panels even more heartwarming than it already was.
For pure heartwarming, notice that the person right next to Vaarsuvius is Inkyrius, his/her recently divorced mate.
Not to mention it means he was probably involved in the same illusion as everyone else. Not his own separate one. Hanging out with Lord Shojo and Mr. Scruffy is his version of heaven.
Elan managing to get the team out of their slump with good old fashioned hope.
"And Elan? Good job. And I'm sorry I snapped at you earlier."
What's even better is that before this, everyone was worried that the because of the whole Unspoken Plan Guarantee the comic tends to lean towards, the story was going to have a total Downer Ending. Elan isn't just assuring his team that things will work out, he's assuring the fans.
901. The Monster in the Darkness saves the four remaining Order members from certain doom tricking Redcloak and Xykon to their faces with a Genre Savvy sounding dose of Blatant Lies. Why? They're pals with O-Chul. And so is he.
Despite now being evil and thus it not working properly, Durkon still goes instinctively to heal an injured Roy. Daww...
Nale's reaction to Durkon injuring and subsequently killing Z is to try and force Durkon off of him and furiously demand that he doesn't suck his blood. While this is what get Z killed, it's touching to know that, like his father, Nale does care for his longtime friends and employees.
Just before this, there's another moment of heartwarming, in which Nale and Z offer friendship to Vampire Durkon as well as employment.
Elan mourned his brother's death, even after all Nale had done.
Sabine's reaction to Nale's death as well.
"I'm not the leader of my team, Dad. Roy is, and he's the best hero EVER."