For a more meta example, take a look at the main page quote from the creator of the show. It's rather sweet that he's found a home for all these discarded characters.
Gumball and Penny's relationship in general is really heartwarming, early on they questioned whether the other liked them too shy to hang out, to Gumball saving Penny from accidentally being run over by her own father (Extra points for being dressed as a knight), Gumball's speech on how when they're together it's like time/the universe stops just for them, the aforementioned Penny standing up for him when he was embarrassed. Pretty much everything that has to do with their relationship is adorable and heartwarming.
In "The Responsible", Gumball decides to take the rap for Anais flooding the house. She's so touched she hugged him and whispered "thank you". But when Gumball was about to say it, he sees his mom's eyes are on fire, so he blames it on Darwin.
During Mr. Robinson's stellar performance, an old man leans over to his friend and asks "Whoa, who is this guy?" and Rocky, Mr. Robinson's son tells him "That's my dad. Rock on dude!"
The ending of "The Quest", right up to where Tina's dad comes up from behind Anais, Gumball, and Darwin.
After getting falsely arrested for robbing a convenience store in "The Spoon", Nicole still has her family celebrating her birthday with them besides her cell. The cops found her innocent after all, too.
The end of "The Painting", where Anais asserts that, even though the drawing she made showed her father as lazy, her mother as stressed-out, and her brothers as destructive, it says "I love my family" and she meant it.
Anais: If you'd listened for a second, you'd know have known that I never wanted anyone to change.
Mom: But I thought you were unhappy, honey. That painting?
Darwin comforting Gumball after he suffers a panic attack in "The Prank"... at least until it gets a little too Ho Yay.
Penny sticking up for Gumball in "The Gi".
Heck, the whole ending is, when Nicole realizes she should never have tried to suppress her husband's spirit and returns his cape.
"The Cottontail Cavalier has returned!"
The last few minutes of "The Party" are nothing but heartwarming:
Rachel thanking Darwin for cleaning up the house by giving him a kiss.
Penny and Gumball about to share a kiss (only to be interrupted by Richard)
Gumball: (waving good-bye and dragging Darwin) Bye, thanks for the party! I love you, Penny! *slaps forehead* WHY DID I SAY THAT?!
Rachel: (blushing) Is that really the best we can do?
Penny: (softly) I think he's awesome...
Finally, Richard having a nice bonding moment with his sons.
Richard: (whispering) I like the new one (Penny) better.
Gumball turns beet red
In "The Picnic", Darwin saves Gumball from the nasty creatures of the forest.
Nobody messes with my team! (Darwin then fish-slaps one of the creatures, forcing all of them to run away!)
In "The Mustache", Richard bought those male supplements that his kids ate by accident because he was intimidated by the internet ads. Nicole hugs him and says she loves him for who he his, and so do his kids. Given Richard's personality and the fact that he felt he was unnattractive, it felt really sweet to hear his family say that about him.
The end of "The Meddler".
Gumball: Mom, you know how I said I wanted to be my own man and make my own decisions?
Gumball: Can it just wait for a few years?
Nicole: The longer the better honey. Even when you're 80 you'll still be my Gummy-puss.
At the end of "The Helmet", Darwin and Anais successfully persuading Gumball to get rid of his lucky hat made out of tinfoil to save him from falling into the garbage crusher when he tries to retrieve it. But it's what Anais says to him that really makes it a CMOH:
Anais: Gumball, we're nothing without you.
The end of "The Fight" when Tina and Gumball become friends.
The end of Hector's rampage in "The Colossus". There's just something sweet about the way Gumball smiles at the sleeping giant, or the fact that for once everyone ends the episode happy and unscathed. Hector's mom isn't even mad.
Darwin kissing Carrie in the Halloween Special. Instead of being offended, she just blushed.
What makes it all the more endearing is the Fridge Logic behind it. Being a ghost and having no physical form, Carrie's interactions with the world around her is limited, with many objects usually passing right through her unless they were ghostly objects. Darwin giving her a kiss after he and Gumball turned into ghosts themselves is most likely a first for her.
And in the same episode, Gumball apologizing to Anais.
The Wattersons enjoying the star that Richard accidentally purchased with all their savings 12 years ago at the end of "The Treasure".
Gumball and Darwin trying to get in trouble so Principal Brown wouldn't have to break up with Miss Simian in "The Apology".
And Miss Simian finding out they weren't trouble makers and apologizing at the end.
"The Hero"..... that's all that needs to be said. Watch it, now.
From "The World", there's a truly heartwarming montage of Anais playing with her Daisy the Donkey toy until the doll starts talking to her.
Gumball telling Darwin that he's totally his brother at the end of "The Words".
Richard giving a grumpy Gumball and Darwin a "Wonder Hug" in an attempt to make them feel better in "The Joy." Too bad things go horrifically downhill from there...
In "The Extras" a colorful bird dances for a black bird but gets dejected and incredibly sad when he finds out the black bird is male. Then the black bird cheerfully tells him the dance was awesome, so he should continue anyway, and the colorful one perks up immediately.
In "The Void," upon realizing that Molly is not only missing but has been erased from everyone's memories, Gumball and Darwin make it their mission to save her even though they can't actually remember her. Especially given that the joke of the premise is that the universe got rid of her because she was such a boring extra (she and the main characters never even talked onscreen when she was on the show), that the two become so fixated on getting her simply because she was their friend and deserves their help is very sweet.
In "The Allergy", when Darwin tries to force Anais and Gumball to leave so they won't be hurt by his out of control sneezing, Gumball refuses to leave his brother.