Anytime Sam does anything heroic. The fact that this is Sam, the girl who grew up with a bad family and followed in their footsteps (though season 4 of iCarly and onwards showed she was straying away from the kind of life her other family members, outside of Melanie, leaned towards)
Sam running down a garbage truck to save Cat in the Pilot.
Sam catching a wanted criminal in #MagicATM
Saving Freddie's life in #TheKillerTunaJump
Despite doing a dangerously bad job of CPR, they managed to save the Inside-Out Burger manager's life.
Sam's flawless Bavarian Fire Drill to get the moving crew to deliver all the decor from the That's A Drag set to Cat's apartment.
Additionally, in the Dutch version of the show, where That's A Drag is known as Soup Dresses, they actually go so far as to insult Nickelodeon. "What kind of stupid network cancels a big hit without a proper finale?!" In the originals, the word stupid wasn't there.
Sam's plan to con the girls who conned them out of 500 dollars and Cat's bike. They trick the girls into going to a bingo match they rigged so that a special card would win the prize of a 3000 dollar TV. They take Cat's bike there. Once there Cat pretends to buy the card until the girls offer the 500 they conned Dice out of. Once the girls win, two cops come saying the bingo game was illegal because the prize was too expensive. They take the girls to a back alley and leave them there. Turns out the police officers are fakes. Cat takes her bike back and Nona (who sold the girls the tickets) gives Dice his 500 back.
Butler, the son of the overbearing mom in #Texting Competition throws the competition after seeing how far his mom will go.
Sam managing to keep up with Butler one-handed, in speed-texting. Girl's got a mad thumb.
Not just that, she beat her own record one handed when her last record was 2 handed.
A smaller one: Sam asks if there's any rule against her texting one-handed, which they quickly check. The guy hosting the show (who's just as annoyed at Butler's mom as anyone), smugly says to her face, "No; there isn't".
The little girl in Episode 6 essentially politely tells Sam and Cat to stop arguing about which of them is better babysitters, as they're a great team together. It helps that the child actress playing her isn't half bad, much like Butler.
When #Pilot first aired, it was the most popular episode on iTunes at the time. By the way? This included all television, not just kids shows, meaning Sam and Cat beat out Mad Men for the top spot.
Goomer of all people figuring out Gwen & Ruby's plot in #Revenge Of The Brit Brats. GOOMER
More of an Offscreen Moment of Awesome, but Sam pulling an entire parking meter out of the ground. It's easy to understand why Dice was impressed
And then she KO's the world's 7th best fighter with one punch.
#Motercycle Mystery: Cat shows us exactly how dangerous she can be, by running/jumping screaming onto the back of a professional MMA fighter (who's trying to steal Sam's motorcycle), and manages to hold him for a good while. After been thrown off, she pins down his smaller friend after he gets away, yells a cop into giving her his handcuffs, and cuffs the smaller man to herself. Then she physically drags him home the entire way, and he shouts something at her, where she responds with "*repeated foreign words*-SHUT UP!"
Cat of all people having the guts to stand up the client in Doll Sitting. Please note that Sam was perfectly willing to let the guy go because of all the crap that had happened that day.
Cat and Sam's twin sister Melanie kiss. ON A NICKELODEON SHOW.
#BrainCrush: Sam using the kids of the karate class to destroy the audience's pear phones in order to make them pay attention to Cat's play instead of the addicting app game.
Cat literally able to create a perfect duplicate of Blue Dog Soda.
The blooper episode. So much self-referential jokes, several moments of Getting Crap Past the Radar, Actor Allusions, Continuity Nods and to top it all off the hilarious bloopers themselves. Oh, and the actors play themselves in this episode (complete with Ariana's normal hair color and general adorableness) and it's glorious.
In #FresnoGirl Sam & Cat got a doll for a girl and end up having to put up with the ridiculous prices (like hair being sold separately) and when they go to fix the doll after Sam accidentally breaks it, the two have to put up with even more annoying prices (like being charged for pretend anesthesia) and after putting up with them, Sam finally cracks and feeds them Cat's fudge piles (which are so chewy it makes swallowing difficult) and when they can't talk, Sam makes an announcement that all Fresno Girl dolls and accessories are free for 5 minutes to get back at the store for their prices
In #SuperPsycho, when Nora has both Dice and Cat trapped, the lights go out only to suddenly come back on and she finds Maurice in the arms of Sam. Jennette's delivery of her line is just perfect here.
Sam: Who wants chicken?
In #KnockOut, Sam becomes Rita Rooney's sparring partner and while Rita, being an MMA champion, has the upper hand for the most part, Sam manages to get her weak spot and knock her down which apparently no other fighter has managed to do, which gives Sam some fifteen minutes of fame.
Sam fighting, some would agree is awesome.
The fact that despite her fifteen minutes of fame for being able to knock down a champion which no other fighter could do, and not actually care about the fame makes Sam even cooler.