Heartwarming: The Order of the Stick aka: Order Of The Stick
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.
However in Start if Darkness he is surprised by Sara saying children in the plural. That means this is before Eric was born. And we all know how that turns out. Or it was after, and he forgot.
There's the other possibility — he worked this out after Eric's (recent) death. So, yes — shock at the coming Julia. Maybe he doesn't just express his love to her openly solely for being mage-material, but is unable to do this with Roy because of their history beforehand. And, a touch of guilt. Just maybe.
Subverted in Xykon's first appearance, we first see him as a four year old crying over his dead dog Barky; when his sorcery powers activate and resurrects 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...
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.
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!"
Tearjerker, 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.