There are many in "Operation: M.A.T.A.D.O.R.", especially the outcome and The Stinger: when Numbuh Four refuses to fight his father, when Mr. Beetles is confused about why he would ever try to hurt his son, the part where he explains how the fathers got in this situation (said dad states they were all going to counseling lessons to be better dads) and Numbuh Four's reaction.
The very end of the series, "Operation: I.N.T.E.R.V.I.E.W.S.":
When Numbuh One is saying goodbye to his parents, who were both recommissioned so that they could better understand the opportunity their son had been given. His mother is understandably weepy but supportive, but seeing the legendary Numbuh 0 try to fight back crying as he wishes his son luck is so touching.
When the rest of the team shows up, they each have their own personal goodbyes. It's not all just, "I'll miss you." "Me too." "Me too." "Ect." They actually feel like real people saying goodbye to a dear friend. It's a real reminder that, even though the show can be funny and awesome, the writers do know how to warm the heart.
The final goodbye between everyone, where Numbuh One asks them to always keep the child inside them alive, and they do the "Five, four, three, two, one. Kids next door!" one last time before saying goodbye.
Back in the interview, the live-action actors have started crying at the memories. Although it quickly turns into a Crowning Moment of Funny, the switch to live-action made the mood seem all the more real.
During the credits, there's a small montage of stills from all the episodes with the theme song playing, which abruptly ends with a watercolor picture of the kids watching a sunset from the treehouse with a single phrase over them: "Stay young..."
Numbuh 5/Abby:Yeah, we told him everything he wanted to hear, we'll meet you up on the Moon base okay? Oh! And Numbuh one? Welcome back.
In "Operation: D.A.D.D.Y.", it was revealed that Mr. Boss is Numbuh 86's father. Despite having being shown as a Child Hater plenty of times before, he claims that he loves his kids (he just hates everyone else's). Afterwards they admitted that they didn't really care if they were technically enemies, that they would just do their thing and still be loving father and daughter. It's both touching and funny.
Another Numbuh 86 one: at the end of "Operation: S.L.U.M.B.E.R.", Numbuh Three, seeing that no-one else is willing to be 86's friend due to her acting like such a Jerkass most of the time, insists that she'll be her friend anyway.
Throughout the entire series, Abby and Cree have had fake-out Crowning Moments of Heartwarming. But in "Operation: V.I.R.U.S." they get to have a genuine moment of sisterly caring, no fake-out, no strings attached.
"You may be my arch-enemy — but you're also my sister!"
Speaking of the Lincoln sisters, anytime there's a flashback to Cree's time as a KND operative. It's both heartwarming and heartbreaking to see a time when she and Abby actually got along.
Any time Numbuh Four almost confesses to Numbuh Three.
In the episode "Operation: M.A.U.R.I.C.E.", Abby goes through a bit of an identity crisis. Towards the end, with her unable to stop the chicken pox machine and two of the people she looked up to the most (Cree and Maurice) now her enemies, it appears she's about to have a Start of Darkness and is about to accept the inevidability of her approaching teenhood as she says, "I can't keep fighting it. I just... I give up." Suddenly the machine starts exploding and her sister falls into the chicken ammo (It Makes Sense in Context). When she looks at Maurice he's holding a marble bomb, and simple says, "Never give up."
And during the credits, after Numbuh Five has learned that some KND operatives keep their memories as they grow up and act as undercover agents, she's looking around at several adults and teens as she walks down the street. For the most part, they just give her dismissive/ugly looks. Then when she comes across some teens hanging around a stoop, the one in the center glares at her for a moment... before winking. Numbuh Five just smiles a little and walks off.
Anytime it's shown that, yes, Nigel and Lizzie really do care for each other. Particular episodes that come to mind are "C.A.K.E.D.-T.W.O.", "P.O.O.L.", "S.N.O.W.I.N.G.", "L.E.A.D.E.R.", and "G.I.R.L.F.R.I.E.N.D." (despite being the episode they break up).
After Sector Z is brought back and told that the effects of the recommissioning module are only temporary the girl with pigtails looks incredibly sad. The African-American guy puts his hand on her shoulder and she reaches up and puts her hand on his hand. It's very brief, but very cute in a sad sort of way.
When Number One plans to use the Recomissioning Module to restore his father's memories of being Number Zero, he gets a holographic message from his dad saying he broke it because, even though he'd like to have more cool adventures with the team, "I'm just not a kid anymore. I'm an adult. And I need to complete the most important mission of my life — being a good father to my son."
"Operation: F.U.T.U.R.E.", "Operation: K.I.S.S.", "Operation: G.R.O.W.U.P.", and "Operation: C.A.T.S." are all also very heartwarming. This show's writers apparently really knew how to portray True Companions.
"Operation: S.A.T.U.R.N." which features a robotic Rainbow Monkey named "Ramon 4" (short for Rainbow Monkeys 4-Ever) that was rejected by kids for being "too ugly" and was sent to outer space... so he steals all the other Rainbow Monkeys from kids. Numbuh Three (who is a BIG fan of Rainbow Monkeys) cannot believe that there is a Rainbow Monkey that nobody loves... so she hugs him showing that he is loved and he lets all the other Rainbow Monkeys go. Awww....
Numbuh Four:(comes out with an umbrella)) Great: now it's raining Rainbow Monkeys! Well, I hope you're [Numbuh Three] happy, now! Numbuh Three:(gazing at the moon) I am... and so is Ramon...
Numbuh Five: Forget it! If "Mr. Uno" wants to act like a jerk for the rest of his life, Numbuh Five say, "Let him!" Numbuh Three:Numbuh Five, how can you be so mean?! You call Numbuh One selfish, but you won't even help him! Numbuh Five: Numbuh Three!... beat Attacking the Delightful Children wouldn't be easy. Numbuh Three: We don't care. Numbuh Five: We don't even have any of our 2x4 technology weapons. Numbuh Two: We'll come up with something. Numbuh Five: We may be turned into adultsourselves. Numbuh Four: No one's a kid forever. Numbuh Five: All right, then — Kids Next Door, Battle Stations!
The Creative Closing Credits was a very nice way to close the first season, showing watercolor drawings of the reunited Sector V spending day and night to fix up their ruined treehouse.
The moment in "Operation: C.A.T.S." when, after an entire episode of refusing to say it, Numbuh Four tells Numbuh Three he loves her. Then he goes back to being completely unable to spit it out, but still.
In "Operation: F.O.U.N.T.A.I.N.", after Leona turns on the kids, tries to de-age them into non-existance, and is about to fall to her death:
Numbuh Four: I thought you saw we came to save Leona. Numbuh Five:(trying to walk away) Change in plans. She's an adult and a jerk. Numbuh Four:(grabs her hand) But she wants to be a kid. A big kid once told me we save kids, that's our job. Numbuh Five: ... Kids Next Door... Battle Stations!
Made especially more heartwarming since for a good chunk of the episode Wally was the one who wanted to give up on Leona and Abby wouldn't let him. In fact it's Abby's words that he is recalling in the above quote.
"Operation: C.A.R.A.M.E.L.". Given all the horrible things that Heinrich has done to Abby (in past episodes, and the stuff he probably did that wasn't shown), Abby still tries to help him and tell him how to reverse the affects of the caramels.
Abby: Heinrich, just share it with me. I promise, it will all be okay. Heinrich:(tearing up) WHY SHOULD I BELIEVE YOU?! Abby: Because... you're more important to me than candy.
Any other moment that showed that Abby still thought of Heinrich as a friend. Like in CHOCOLATE when, even after arresting Heinrich, she brings him the one food he's been craving for for weeks but couldn't eat due to his previous condition.
During "Operation: P.O.O.L.", when Numbuh Four's friends get switched with negative doppelgangers from another universe, Numbuh Four only manages to figure it out by looking into Numbuh Three's eyes, which are filled with cruelty that the real Numbuh Three does not possess. Ergo, they must be from a negative universe, he figured that out by being a friend! It's incredibly cheesy, but still sweet.
The only other character to figure this out was Numbuh 1 after realizing that Eizzil didn't have the same look as Lizzie, which goes to show just how special Numbuh 3 is to Numbuh 4.
"Operation: O.O.M.P.A.H.". As Monty's first appearance, there's plenty of these.
Nigel: I'm sorry, Dad. Monty: That's okay son, you did your best. And according to the Dad's Do's-and-Don't section of the paper, that's all that matters.
Monty himself is also heartwarming when you consider the type of father he had. He literally has had no good father figure, but he still tries to be the best father to Nigel that he can be (reading articles on how to be a father, trying to spend quality time with him, etc.). Seriously, he could've easily turned out like his brother.
Moosk's sacrifice in "Operation: K.N.O.T."
Numbuh Four: Numbuh One, who was that guy? Numbuh One: A comrade...
Throughout the entirety of the episode "Operation: D.O.G.H.O.U.S.E.", Abby tries to deal with the problem of the episode herself, and is even seen crying during the episode. When Wally tries to help, she keeps pushing him away. Finally, when he finds her at the bottom of the steps of the haunted doghouse:
Wally: Numbuh Five, are you okay?! Abby: Numbuh Four, what are you doing here? Go back to the treehouse! Wally: No way, my homework's in there! Along with whoever did this to you. Come on, you and me can— Abby:(voice breaking) I said go home! Numbuh Five can handle this herself... Wally: I know you can. But two of us can handle it better. Abby: Number Four! .... (looks up with teary eyes) Help.... Wally:(smiles)
Pratically all interactions between Abby and Wally in the episode count as this. Like Brother and Sister was in full effect here.
In "Operation: P.A.R.T.Y.", it's about the only time the Delightful Children seem genuinely grateful for the Kids Next Door's help, but it's still nice to see.
Decommissioning may be scary, especially in context of the show, but think of it this way: these kids sign up knowing that they will lose all memory of a considerable chunk of their childhood, all of their adventures and friends, in order to protect the right of other children to, well, be kids. A Heroic Sacrifice indeed.
"Operation: B.U.T.T.": Not only Wally is visibly sad for Numbuh One leaving the team (to the point of crying), but when he sees how upset Kuki is, he tries his best to cheer her up using her stuffed animals and making sweet voices, even if he HATES them. It was his fault getting her to cry because he snapped at her missing the context of his leaving, but, if anything, that makes it even more heartwarming. He immediately realized his mistake and wanted to fix it for Kuki.
Real Life incorporated into the show: a Make-A-Wish Foundation patient named Jacob "wished" to be in an episode of KND. Jacob appeared as a scientist named Numbah 275, albeit only a few times and with no spoken lines, in the second half of "Operation: F.E.R.A.L.".
Throughout Operation: I.T., Numbuh 1 refuses to give up on Numbuh 362 during her episode-long Heroic BSOD. The show never gives much detail as to exactly how far back they go, but it's clear he's just as close with her as any of his team. There's a perfect example about five minutes in where Numbah 1 asks Numbah 362 why she gave up the job. She reveals how very exhausted she was by it and how she didn't want to deal with the stress anymore. Numbah 1 adamantly tells her that he thinks the job is perfect for her and makes it very clear he thinks she should take it back. Numbah 362 politely refuses and holds out her hand for him to shake, at which point Numbah 1 reveals he was It all along, tells her she probably doesn't want to touch him, and leaves the bridge, still It. He could've forced the job on her at any time in the conversation, but instead tried to convince her to take it willingly.
When Rachel wakes up in the Moon Base infirmary, Nigel's sitting right by her bedside. He explains she's bene out for a week — was he waiting by her side the whole time just to be sure he'd be there when she woke up?
Ever wonder why Numbuh 3 loves Rainbow Monkeys so much? Well, in "Operation: C.L.U.E.S." we find out that her mother bought her them because she never had any dolls as a girl herself. And in "Operation: H.O.M.E.", we find out she had her first one since literally seconds after she was born. It's epecially nice since, before revealing that bit of herself, Numbuh 3's mom looked like a no-nonsense angry boss.