In the first story arc, after the teens' second encounter with their evil parents:
Leslie (Karolina's mom): You think you've beaten us? We haven't even used a fraction of our strength against you. One the kid gloves come off, your parents will annihilate you. We brought you children into this world...
Alex Wilder: And we can take you out. (knocks her out with a big magic stick.)
An early one for Karolina: When one of the parents questions whether or not the kids will fight them, Leslie Dean scoffs and says that Karolina doesn't have the spine to fight. Later, she goes to confront Karolina. Leslie imprisons Chase, and just cranks up the honey and sugar: she greets her daughter with "Hello, my angel," and explains that yes, K, you're an alien, and you'll learn more about your beautiful gifts, and that there's no point in fighting because their abilities are exactly the same and can't be used to hurt each other. Karolina, angry that she's been lied to and upset that her life isn't what she thought it was, takes the power limiter bracelet, and says that if her mother's powers are the same as hers, the bracelet must also do to her what it does to Karolina: "Take away everything that makes you special." And she brandishes it like brass knuckles, pulls her fist back and clocks her mom right then and there.
Villainous example: Alex Wilder's revelation at the climax of the first volume of his excellent Evil Plan, as well as gaining the powers of half the titular team. Granted, it doesn't last, but it was pretty awesome.
The cherry on top of this being The full page shot of Alex with the fistagons, Chase's goggles, the Staff of One and Old Lace behind him, giving a Kubrick Stare after giving one hell of a Badass Boast. As evil as betraying his friends was, you have to admit he did it with style.
Alex: The mole? Call me whatever you want but I just saved you two from getting offed by a few of your so called friends. It's a long story, but like I said it's about to end. I'll explain everything After we finish the rite of thunder.
Geoffrey Wilder: But Alex, the rest of the pride
Alex: you don't need them anymore Dad. You've got me. Aren't you proud?
Nico's followup to the above's full explanation, as simple as it was, did even more. After being offered so much by Alex and hearing the full explanation of his evil plan, including his wish to be with her forever in the paradise the Gibborim promise, she just punches him in the face.
Nico: Not if you were the last boy on earth. Loser.
And following that The quick turnaround the team makes: Karolina, upon being informed of the situation, blasts Alex. Alex quickly chains her up with the staff of one and plans to have Old Lace dispose of her.. only to find out Gert's woken up, taken control back, and is none too pleased about the betrayal, having Old Lace return the staff of one, which Nico promptly uses to destroy the fistagons.
The team's break-in to rescue Old Lace from an old West Coast Avengers storage unit following the deaths of their parents and Alex, and all of them being remanded to foster care, taking out a bunch of security robots with ease and then deciding to run off together afterwards.
In the said break-in, Nico defeats a large security robot not by using her staff, but by stabbing it in its eye with a knife! Chase even exclaims that it's the "third coolest thing he's seen in his life".
The Second Series:
Chase has a pretty big one.
Chase: (the group has just detained Victor) Don't worry this psycho killer ain't going anywhere.
Victor: What's... what's your power?
Chase: A poor upbringing. (brandishing knife)
Darkhawk wasting Ultron was sweet after everything the droid did.
In the first New York arc, Molly punches Wolverine out of a church and into a snowbank across the street. Also doubles as a Funny Moment.
Chase, when dealing with the Cloak impostor, using the Staff of One.
A shopkeeper accidentally becomes a huge destructive giant through some magical artifact. When its determined that they can't beat the giant through simple head-on combat, the team uses the voice and image of the shopkeeper's dead wife to convince him to stop the violence and change back to normal.
In the Live Fast arc, Chase is scary-good at acting like a villain. He's decoded enough of the Abstract to find his way to the Gibborim's limbo dimension, abducts Lotus, and later on, ties Nico to a chair and incapacitates Victor with a Logic Bomb he found from the abstract.
In the ensuing confrontation, Karolina is able to convince Old Lace to stop following Chase's commands.
Victor and Molly using the Fast Ball Special to save an unconscious Nico from being eaten by the Gibborim.
Even the team's psychic dinosaur gets its own CMOA. After Chase fell off a building, Old Lace managed to grab him by the jacket, dug her claws into the building, and ran up it to get Chase onto the roof. Made even more awesome because while the rest of the team is wondering if Chase and Old Lace just died, Molly guesses exactly what happened.
During the second New York arc, the team runs into The Punisher, who decides to threaten them with a gun. Molly floors him with a single punch.
Chase stopping the Yorkes from stealing the Leapfrog using their own tech, getting a new set of fistagons in the process.
The Third Series
Molly punches a Super Skrull through a skyscraper during Secret Invasion.
In the first issue of the third series, a guy is thrown over a railing while the Runaways are visiting the mall. Klara, without hesitating, saves his life.
Klara: Grow! (A bunch of palm trees spring up and break the guy's fall.) Lie down. Thank you.
Klara's leap in character growth may be considered one too. Despite initially being freaked out by Xavin and Karolina's lesbian relationship, here she thanks the former for something, and acknowledges that the later had saved her. And Klara cheers Nico on for using magic, despite coming from an ultra conservative Christian traditionalist background.
In the first issue, Nico manages to prevent Gert's death.
In the fifth issue, Molly reminds everyone she's smarter than she lets on when she reveals to Gert she knew all along her grandmother's cats have been engineered to read minds and keep tabs on them, and she was the one who gave her parents their powers. Molly managed to fool her grandmother for months into thinking she didn't know she was being watched the whole time and is prepared to run away with Gert to save her from being experimented on.
The Seed of the Gibborim demand that the Runaways follow in their parents footsteps and sacrifice innocents to them and if they refuse they will form a new Pride and use them as the sacrifice and the Runaways stand defiant and ready to fight.