The awkward but endearing relationship Dave has with his father, who does his very best to be there for his son, even if kept in the dark about all the heroics.
Mindy's therapist tried to get her "cured" by showing her mother was ashamed of her. But when he finally tricks Mindy into meeting her, her mother tells her that not only she's proud of her fighting crime, but that knowing she's her mother she made her stronger and drove her to help at a local shelter.
In the final issue, Dave finally gets his happy ending, along with sorting his life out.
Chris and Mindy's mothers bonding over their children being costumed killers. You can also theorize that Mrs. Genovese learned that Chris died to save Mindy's life, which added to their friendship even more.
The film
Kick-Ass defending the guy outside the store is both awesome and heartwarming. He gets involved in the guy's business completely by accident, but he sees him getting ganged up on by three thugs and decides that, contrary to what one of the thugs says to him, this is his business. He doesn't know the guy's history, why he was being chased, or why he's getting beat up; he also hasn't really refined his fighting skills. He simply jumps in and helps the guy out because it's the right thing to do.
Thug: What the fuck is wrong with you, man? You'd rather die for some piece of shit that you don't even fucking know? Kick-Ass: And three assholes, laying into one guy while everybody else watches? And you want to know what's wrong with me?! Yeah, I'd rather die! So bring it on!
This successfully gets the thugs to leave, and we then see the guy Kick-Ass was protecting say "Thank you" to him. One gets the feeling that that's what made fighting worthwhile for Kick-Ass.
Hit-Girl's final moment with Big Daddy as he dies.
Their whole relationship throughout the movie (and comic) is adorable in a very Addams Family kind of way.
The music during the gun battle just prior as well - the action is her dishing out awesome, but the music is channeling Big Daddy's pride watching his daughter slaughter everyone.
Not to mention, even as Big Daddy is burning to death, he keeps shouting encouragement and advice to Hit-Girl.
Hit Girl wonders why the bullet hitting her bulletproof vest hurt a lot more than she remembered, only for Big Daddy to tell her he used low velocity rounds. Despite training her to be an efficient killer, he never wanted to seriously injure his daughter.
Big Daddy believes he is about to die having failed his daughter. But when he's set alight and sees her alive before him; he has no thought of his own pain. And those three words.
Big Daddy: TAKE COVER, CHILD!
In the film, Katie forgiving Dave for lying about his sexuality and letting him spend the night (and share the bed).
Even though Frank is a cold-blooded killer, there are several moments where you can tell he really loves and cares about his son. Like when he thinks Chris died in the lumber mill and their reunion hug. Just look at the relief on Frank's face when he sees his son is alive.
"Listen, my son's waiting in the car and wants to see a movie. I'm not going to disappoint him."
When Kick-Ass meets Big Daddy in person, the first thing that he says is "We like you, but we don't trust you." This is rare because the only people he expressed any affection for is Hit-Girl and Marcus. It's further lampshaded by Hit-Girl later on after Kick-Ass saves her and kills Frank, when she says that he would have been proud of them both, rather than just her.
Chris asking his dad and his men to let Kick-Ass go is kinda sweet.
In the film, Marcus gives a satisfied smirk when he saw Mindy slaughter everyone on the broadcast, as if to say, "That's my girl."
