It's a small moment, but when the Runaways' first hideout gets raided, Karolina instinctively moves to protect Molly.
The Minorus holding off the Gibborim just long enough for the kids to escape.
Tina Minoru: I'm still your mother, you will do as I say.
The team reuniting after their parents, and Alex's, deaths and being sent to various foster homes, particularly Chase, who spent months tracking down Old Lace for Gert. Followed up right after they break her out, with the entire team choosing to stay together, as a family.
The Second Series:
Nico's first inclination when they learn Victor will become evil in the future isn't to rush off and kill him, but to try and make sure that doesn't happen since he's like them. She also welcomes him into the group once he becomes an orphan, same as them.
Molly Hayes has these constantly. More specifically, at one point after Gert's death, she asks the team's car (well, giant frog-robot, but you know) if Gert is in Heaven, and when the robot replies that its GPS program can't locate Gert, this upsets her... but then the robot reprograms its GPS so it can say "Location: Heaven, confirmed". It is so very sweet.
The Young Avengers/Runaways Civil War arc has a couple.
After Xavin rescues the others from being cut up by the Mad Scientist, they proceed to nearly kill said scientist. Teddy stands up to them and insists that it would be wrong and Karolina throws her arms around Xavin when they back down. Later, Xavin thanks Teddy for stopping them, explaining that they realized if they went ahead and killed the scientist, they would have lost Karolina. They also give this extremely sweet line:
Xavin: She's beautiful, isn't she? Karolina. She's so soft and tender. She's all that's good in my life...
Later, while the Runaways and Young Avengers are fighting to escape the lab, a brainwashed alien attacks Old Lace, hurting Chase as a result. To save them, Molly fights off the alien and is thrown against the floor, pretty much leaving her unable to fight back. Chase holds her, assures her that she did good, and promises to protect her. He then turns and fights the alien to keep it away from her. Keep in mind that before this, Chase was still recovering from the death of Gert and had very little patience for Molly.
Nico delivering an impromptu eulogy for Chase after thinking that he's been blasted off of a rooftop is rather sweet.
In "Dead-End Kids", Molly goes to considerable lengths to keep Klara comfortable as Karolina tries to coax her story out of her, like covering for her when she makes a mess while eating or playing dumb when Klara talks about having to perform "marital duties" for her abusive husband.
The Third Series:
During the "Dead Wrong" arc, when the team is under a spell that causes them all to act impulsively, Molly's impulse is to take Klara off for a picnic. It's one of the few times in the entire series that Klara looks genuinely happy and at peace.
In the "Dead Wrong" arc by Terry Moore, there's another heartwarming moment involving Karolina and Xavin. Karolina is being chased by Majesdanian soldiers who hold her responsible for the destruction of their home planet. She finally decides to stop running and give herself up. Cue the team's hardy protests and Karolina's insistence that she has to go and explain to the Majesdanians what really happened between them and her parents. Then, just as the tears are falling, Molly caps it all off by doing this:
Molly: I want to give you a going-away present, but this is all I have on me. I got it from a box of cereal.
Karolina: A compass?
Molly: You might need it to find your way back to us.
For icing on the cake, we find out on the very next page that it was Xavin, not Karolina, who went with the Majesdanians. All because of their love for Karolina.
Xavin: I will take your love with me, Karolina. They will see you in me and realize... we are the way to a new world.
It's also quite possibly the first and only time in the entire series that the two of them share a kiss on-panel.
As "Karolina" says her goodbyes before handing herself over to the Light Brigade, Klara tells her that she wouldn't be there without her. When the real Karolina emerges, distraught, Klara immediately rushes to comfort her.
When Gert finds out that Victor died, she insists that they give him some sort of burial, even if it has to be in effigy.
The first few pages of Issue #3 reveal that Karolina and Julie Power are still together.
Even with the mess that pulling Gert ahead in time, Chase promises not to abandon her and Nico still intends to be with them since they're her world.
Victor doesn't hide the fact that he's awake from Molly when they first met.
Mixed with Tearjerker, but when the group finally went to bring Klara back with them, it turned out she was placed in the care of a married gay couple and is quite happy where she is. It's clear her foster dads love her and she's finally grown out of her antiquated beliefs on queerness, apologizing to Nico and saying the group showed her love is all that matters. While it's sad she doesn't wish to return, at the very least Klara's managed to find a sense of stability she's most likely never known and is in the care of two adults who are a far cry from her abusive mother and husband.
As a parting gift to her friends, Klara gives them all flowers. Gert, Nico and Chase get a flower each because they are friends, Karolina and Old Lace get flower crowns because they saved her life before, Victor gets a flower necklace because he taught her how to play (and cheat at) video games, and Molly gets an absurdly large bouquet.
In Issue #12:
Gert is feeling depressed and wants to use her time machine to get away for a little while, so Victor helps her hotwire it. The two then go to a field in the past to see an extinct species of butterflies and then just talk to one another about their problems, with Victor confessing his Accidental Murder of his nephew. Gert reassures him that it wasn't on purpose and the two kiss one another as Victor confesses that she makes him feel like a person again.
Nico and Karolina also get together, complete with The Big Damn Kiss, after over a decade (for us) of build-up - which is driven home by the issue starting with a flashback to the Almost Kiss way back in "Starcrossed".
The short story "It's Not Lupus" ends with Nico reading a bedtime story to an exhausted Molly and Klara.