The end of episode 2, where Shaggy holds Velma's hand reassuringly while Scooby Doo holds onto him all scared. Seeing Velma smile like that makes you melt inside... and hope that things get better for those two later on in the episodes.
Episode 4, we get the first real indications that maybe Fred likes Daphne more than either of them realized...
First he makes a comment about the "man-crab", asking what man-crab wouldn't want to capture her?
Then, after said man-crab does, in fact, capture Daphne, Fred goes into a Heroic B.S.O.D.. He spends hours digging, wherever he is, including in the Mystery Machine and Velma's room, since she was dragged under the sand at the beach, and then spends the next several minutes making random comments about Daphne.
Fred: There's a book over here... Daphne read a book once!
Fred: And this chair... Daphne liked to sit in chairs!
Fred: That card catalogue over there-
Velma: Not helping, Fred.
Fred: I know, what's the matter with me?
Freddy's realization in episode 7 that he cares for Daphne as much as he does traps. When he can't reconcile this with his belief that real men don't have feelings, he declares that he isn't a guy anymore, putting his feelings for her over his need to be "macho".
In episode 12, despite constantly mocking H.P. Hatecraft and dissing his writing, Harlan Ellison shows up concerned for his safety when the monster kidnapped him. After Hatecraft is rescued and the bad guy caught, they have a Not So Different moment when they realize they both have Loony Fans, and Ellison proposes they co-write a book about said fans.
Daphne hearing Fred call her his girlfriend during episode 13, and showing that she understands how much trouble he has with expressing himself.
Scooby apologizing to Velma for all the trouble he's caused in Velma and Shaggy's relationship.
Episode 15: When Daphne says her heart will always belong to Fred.
Another moment in episode 15 is when Maxwell kidnapped Velma and Scooby. He wants Velma to hack into the National Train Database and he gets her to do this by threatening Scooby's life by hanging him from tree over a cliff with sharp rocks at the bottom. When he's about to drop him Velma begs him not too and agrees to his demands. The dialogue explains it all.
Velma: Wow. Kind of ironic?
Scooby: Yeah, Ironic. (beat) What does ironic mean?
Velma: It means: here's the chance I've been waiting for. To get Shaggy back! All I have to do is refuse to help...
Velma: (Immediately reassuring-sounding) But there's no way I'm going to take it! Even though you stole my boyfriend, I'd never let anyone hurt you, Scooby-Doo.
Scooby: (laughs) Never a doubt in my mind!
Episode 16: This exchange between Daphne and Fred.
Daphne: (referring to being under the love spell) How much do you remember?
Fred: What do you mean? All of it.
Daphne: Really? And how does that make you feel?
Fred: No different.
Fred: I don't need Aphrodite's spell to care about you.
Daphne: *happily* Oh Freddy!
Velma, to Mai Lee after she's been caught in Episode 18:
Velma: He's too good for you! Dog issues or no dog issues!
The end of episode 22 - a bit of a breather from all the dark stuff going on. Sheriff Stone even has fun!
Pretty much the end of episode 24. Even with the Night Ranger doing a funky jig at the end.
For the twists and turns and depression that was episode 26 Mayor Jones rescuing Fred stood out for this troper and showed that even with all the abuse and neglect that he put him through, he still cared for Fred's safety.
When the gang gets back together at the end of Episode 29 after the culprit was unmasked.
Daphne returning Judy's locket to her in "Hodag of Horror", which greatly touches Judy. It becomes something of a Tearjerker when, at the end of the episode, Professor Pericles instigates Judy and Brad's Face–Heel Turn, meaning that such touching moments with them won't be happening again.
The flashback with Ricky and Pericles in episode 33.
Also, Velma hugging Scooby in that same episode. They've certainly come a long way.
The friendship between Velma and Hot Dog Water (Marcie) in Season 2 is made of heartwarming.
Despite the gang's anger at Cassidy they all come running when they think she's in danger in "The Midnight Zone."
The fact that almost everyone in Crystal Cove, even the imprisoned villains from Mary-Ann Gleason all the way up to Ex-Mayor Jones, the previous season's Big Bad, helped the gang with their plan in "Wrath of the Kampus".
Episode 43, "The Horrible Herd", and in general, the growing romance with Sheriff Bronson Stone and Mayor Janet Nettles; what started as distrust and dislike turned into a genuine and adorable growth.
Sheriff Stone: Can I play co-pilot? Because, well... I literally have no idea how to fly a helicopter.
Mayor Nettles: Sheriff, you can be my co-pilot ANYTIME.
Given the amount of guest stars from previous Hanna-Barbera cartoons, this series could count itself as a CMOH, simply for the sheer amount of nostalgia it envokes. From Tom, Tub, Scooby, and Moby Dick, to Blue Falcon and Dynomutt the Dog Wonder, to Race Bannon and Dr. Benton Quest (with a nod to Bandit thrown into their dialogue), and even the guest stars of the Dream Sequence episode (Jabberjaw, Speed Buggy, Captain Caveman, and the Funky Phantom), our favorite shows haven't been forgotten.
Episode 44, "Dance of the Undead"
Daphne: Where's Scooby going?
Shaggy: Where he goes every day, five times a day. To visit Nova.
In "The Devouring," Fred is the one (out of everyone) who encourages Dr. Rick Spartan to call his wife and begin a chance of reconnecting their relationship, in the process simultaneously beginning to rekindle his relationship with Daphne.
In "Stand and Deliver," the Highwayman holds a group of people at gunpoint and orders them to put all their valuables in a bag. Shaggy is present at the time, and instantly points out that his only "valuables" is Scooby.
Episode 48, "Nightmare In Red": In the dream realm, Fred reconciles with Fred Jones Sr., or the "better side" of Fred Jones Sr. who admits to Fred that he's proud of him and that being his father was the best part of his life. Fred literally was the best part of him.
El Agguire breaks down sobbing, adamant that the Nibiru entity shouldn't be destroyed solely because the horrific acts he and his men have performed under its influence have damned them, and they deserve the punishment of being lost in the Sitting Room with no salvation. The Annunaki inhabiting Nova soothingly reassures him that, when Mystery Incorporated does defeat it, all of his misdeeds will be forgiven. It turns out to be because he will have never committed them.
Episode 49, "Dark Night Of The Hunters": Velma's heart-to-heart with her mother at the end and their hug. After her near-meltdown in episode 48, Velma needed that.
Episode 50: Fred comes right out and tells Daphne he loves her. It moves Daphne...and Velma...to tears.
Also Sheriff Stone comes out and tells Mayor Nettles that he loves her, also making an epic Rousing Speech to get the citizens of Crystal Cove to fight back at Pericles' robot forces.
Shaggy volunteers right away to start a prisoner uprising on the spot, then wonders what that weird feeling in his chest is. Scooby replies "Courage."
Daphne comforting Fred after he is forced to destroy the Mystery Machine.
Fred: What have I done?
Daphne: What you had to. What you always do. Turned traps into a fighting chance to live.
Even the villains get their share of heartwarming in this episode. Mr. E nostalgically looks into his own journal and wonders what happened to Cassidy, showing that he wasn't involved in her death and still deeply cared for her even after the curse. A look into the journal also shows that Pericles seemed to be jealous of Cassidy stealing Ricky's attention when she first met him (paralleling Scooby's jealousy of Fred and Velma), showing that the psychopathic bird once had a great deal of affection for his owner.
The Series Finale. Upon destroying the Nibiru Entity, it's erased from history, and everyone's lives turn for the better. Sheriff Stone and Mayor Nettles are married with four children, Fred's birth parents aren't psychotic and Daphne's parents now support her's and Fred's relationship, Shaggy is now an award winning chef, Ricky Owens owns a successful and environment friendly company, is thin, and married to Cassidy, and even Pericles isn't insane or evil.
Also, Fred Jones Sr. is a coach at Crystal Cove and considers Fred to be like a son to him, and Marcie is Velma's best friend, and the two have won dozens of academic awards together. The clincher about that last one? When Velma has a Eureka Moment about what has created this new timeline and rushes off to tell the Gang, Marcie simply smiles and says "That's my girl."
Before all that, the group realizing what the 'Heart of the Jaguar' really is: their bond of friendship. They rally one another before rushing off to put down the Nibiru Entity once and for it together, as a team.
Nova, still under the control of the annunaki (presumably) watches Mystery Incorporated leave Crystal Cove one last time, and declares Scooby the bravest dog ever. Truly high praise from such a being who watched the gang save the world.
Even more so seeing as the Annunaki are Time Abysses, meaning if anyone can make that statement and it be Not Hyperbole, it's one of them.