Cosmo and Wanda's song in School's Out!: The Musical, So. Very. Much.
Then it becomes hilarious when Cosmos says this.
Cosmo: Yep. "Operation: Distract Jorgen with a sappy love song" works every time!"
Also in that movie, the two have to return to Earth through the rainbow bridge, but it only has enough space for one. In a move of heroism, Cosmo pushes Wanda so she can go to Timmy, while he gets captured by the Pixies.
In Wishology Part 2, where Timmy sacrifices himself in order to save his family, friends AND his enemies. Everyone is heartbroken and when Timmy is sucked into the Darkness they all cry TIMMY! even Jorgen and Crocker who rarely call Timmy by his first name
In the Superbike episode, Timmy's dad worked hard to make him a working bike, but feels sad when Timmy doesn't use it. Timmy's mom explains that she could buy stuff at the store, but she decides to use her husband's inventions to make him happy. This causes Timmy to dismantle Superbike and use the trash bike his father made for him.
The episode Bad Heir Day where Mr. Crocker of ALL people bonds with Poof. Upon discovering he's a fairy, instead of destroying him, he returns him to his parents. Denzel Crocker is very heartbroken because he has bonded with Poof even to the point of calling him D.J. or Denzel Jr and states that despite his need to capture fairies, he wouldn't go as far as to steal a child from their parents.Yet the sadness is taken away and he gets a Crowning Moment of Funny (sort of..) when he yells "FAIRY IN THE HOLE! and shoots Poof. Also when Poof poofs up a robot son for him because he sees how saddened he is.
Poof's little squeak of "Crocker" really just drives it home.
Made even more heartwarming/sad when Poof hugs Crocker...and then Crocker starts crying.
How about the end of "Abra-Catastrophe" where Timmy is reunited with Cosmo and Wanda (pictured above).
Cosmo: I'm Cosmo
Wanda: And I'm Wanda!
Both: And we're...your Fairy Godparents!
Timmy: And I wouldn't wish it any other way!
The Valentine's Day special "Love Struck" featured a very heartwarming moment when, after Timmy had been rejected by Trixie and laughed at by the school, he later learns that Trixie wanted to be his Valentine anyways and is poised to accept, but when he notices lonely Tootie crying on a park bench nearby and realizes she deserved his love more than Trixie did after being rejected and humiliated by her so many times. So he leaves Trixie with what the creators described as "the mother of all snubs" and spends his Valentine's Day with a delighted Tootie.
Another Tootie and Timmy one is "Boy Toy". Timmy gives up his Crimson Chin doll to Tootie so a) she doesn't feel sad and b) she never, ever follow me home again. He even adds that it would be their secret of love.
Which becomes hilarious when Tootie arrives with a wedding cake topped with both the Crimson Chin doll (with a pink hat) and a doll looking similar to Tootie and makes them kiss each other.
"Apartnership" was a very sweet one. Mama Cosma is angry that after going through a date show simulation for Cosmo (long story), she begins her rant about how much she hates her. Cosmo steps in and says "Let's get something straight! I'm not bright! Big words confuse me! I have the attention span of a rodent! But Wanda loves me anyway. She makes me happy and THAT SHOULD BE ENOUGH FOR YOU!"
This is lampshaded when the audience is supposed to say 'Awww...' at the heartwarming scene.
Don't forget the episode where Timmy runs away and joins the circus due to overhearing his parents complain about how much nice things they could get without him. In reality, they were just saying those things as examples of what they think isn't true, as yes, even if they do covet the Dinkleburgs' gadgets, they prefer having Timmy instead. In one part of the episode, Timmy looks through a magic mirror to check up on his parents, and sees them tossing his clothes out of the window. Timmy breaks the mirror right before it's revealed they were just making room in the closet for the new clothes they bought Timmy. And after being chased by the carnies for one-upping them, he ends up back at his house and looks through the window to see his parents crying because they miss him. It's at this point that Wanda and Cosmo reveal that the carnival and the chase were all part of a Batman Gambit to get Timmy to realize that his parents really love him, and the carnies were all fairies in on it (except for the alligator man) Looking back, I'd say it's a moment where Mr. and Mrs. Turner actually show that they care about their only son.
A simlilar moment happens near the ending of "Channel Chasers". After Timmy saves the world from Vicky, his parents take over all of Dimmsdale's TV stations and broadcast a message to Timmy declaring their love for him.
The speech Timmy gave about why he loves Cosmo & Wanda in "The Zappys!":
"Why? What do you mean why? They're my best friends. Well, they make me feel safe. They make me feel special. They make me feel loved. They may make a few mistakes, but they're my pals, and I love them more than anything."
Another sweet moment comes from the Thanksgiving storybook, In a Tizzy over Turkey! Timmy spent the book wanting to eat a "proper" Thanksgiving dinner with actual turkey (because his mom made turkey-flavored tofu this year), but of all the people to teach him that he should be spending the holiday with family, it's Vicky, who in is actually sad that she's apart from her family today. In the end, Timmy brings Vicky and her family over for dinner at his house.
Another heartwarming moment from the books is in the Easter storybook, Timmy's Eggs-Ray Vision. After using x-ray vision to find as many chocolate eggs as he can, Timmy sees Vicky pushing Tootie over and stealing her chocolate eggs. But rather than ignoring this, Timmy actually goes over to Tootie and gives her a handful of the chocolate eggs he found.
In the episode where Timmy wishes that he was wanted more, all the fairies engage in a cage match to see who will be his fairy godparent (by throwing shoes at each other's behinds). Timmy notices that Cosmo and Wanda aren't affected by his wish and asks why. Wanda simply says that she and Cosmo couldn't want him more even if they tried.
It gets better. For this heroic act and his acceptance into adulthood, Timmy gets to keep Cosmo, Wanda and Poof! So long as he and Tootie use their wishes to help everyone else around them wherever they go. Fairy Council sure loves that new man now...
In the only episode that ever focuses A.J.'s and Timmy's friendship, the scene at the Academic Brain-A-Thon when Timmy goes up to moderator to disqualify himself because he cheated (in actuality used Cosmo's and Wanda's magic) but A.J. stops him by saying to the moderator:
A.J.:"What he wants to say is he would like to switch chairs".
Timmy:"Yeah what he said; he's the smart one".
A.J.:"And you're the fast one; I'll be the brains and you be the reflexes".
That brief scene,in my mind, has always shown they are the best of friends.
When Vicky threw herself between Timmy and what she thought was an abominable snowman to protect him. This moment surprised me as much as it did Timmy.
"A Boy Who Would Be Queen" is a personal favorite of this troper, especially Trixie and Timmy, er, Timantha spending some quality time together, with Trixie revealing some Hidden Depths about the typical "girls can't do boy stuff and vice versa" Double Standard and Timmy trying to break from said standard.
The last few minutes of "For emergencies only" are full of this.