Kirby: Right Back at Ya! had a few that come to mind, the first being Kirby's Pet Peeve when Kirby's robotic dog- whom he had bonded with over the course of the episode- exploded. Even worse than that is when Kirby is sitting on the beach that night, looking almost as though he's unable to comprehend its death. Then he sees it as a constellation, running away from him.
Kirby Takes The Cake, anybody? Sure, the ending's upbeat, but Kirby still runs away from Cappy Town after he's led to believe nobody likes him by Tokkori, and then cries (Yes, CRIES- tears and all, as seen in the page image.)- after remembering the good times he spent with his friends, whom he thinks have abandoned him.
Meta Knight's stories of how Knuckle Joe's Father and Sirica's mother Garlude both died. Knuckle Joe's Father is stated to be one of Meta Knight's old friends from the Galaxy Soldier Army, whom he had to Mercy Kill after being turned into a Demon Beast by Nightmare, whilst Garlude was one of his closest allies in a mission to retrieve the legendary sword Galaxia from the great beast Kirisakin. The mission goes wrong when Kirisakin awakes and attacks the two, resulting in Garlude performing a Heroic Sacrifice to save Meta Knight- knowing that he was the one worthy to wield Galaxia- fighting off the great beast and throwing the legendary sword to him just before it kills her.
The entire funeral scene in D'Preciation Day. The original Japanese version was even sadder because of the music and the somewhat realistic crying.
The backstory that's gradually revealed to us in the series is quite sad from Meta Knight's perspective. Nearly all of his friends are dead as a result of the previous war with Nightmare's monsters, had to kill one of those friends himself and watch another sacrifice her life for him, and the only remnants of his old life as a warrior are an old man who's been stranded on an island for years (Kit Cosmos), two children that want to kill him as they blame him for their parents' deaths (Knuckle Joe and Sirica), Sword and Blade, and a baby warrior that can barely speak, let alone fight without an Ability handy (Kirby). Wow.
The entirety of Forgotten Escargon (Escar-Gone in the dub). Escargoon has been possessed by a demon beast known as Boukyakou/Erasem. Whoever it possesses will be forgotten by everyone they know. Poor Escargoon has been looked upon as a stranger by everyone he knew, from King Dedede to the Waddle Dees to all the citizens of Cappy Town to even Meta Knight. The clincher is when he bumps into Kirby- who isn't the most fluent communicator in the world, to say the least- but his replies of "poyo" allow Escargoon (who was getting desperate by this point) to finally seek some comfort when it looked like Kirby knows who he is. By the time they bond at the beach, Escargoon sees Kirby as his kindred spirit.
Of course, if you have a cruel enough mind, it's possible that Kirby really had forgotten Escargoon, and is just being nice because that's just how he is- but still speaking the way he always does. Not helping are the implications that this whole ordeal is making Escargoon feel suicidal.
Escargoon: There's no point in living if no one knows who I am.
When Mable predicts the planet's destruction via collision with a giant meteor in Prediction Predicament (Part Two). At the meteor gets closer and closer, everyone resigns to their fates, and decide to all come together at Dedede's castle. There, they begin confessing and apologising amongst one another for past grievances and for anything they did wrong to each other. Doubles as a Heartwarming Moment.
This also leads to one of Dedede's most humanising moments- when he decides that before he perishes, he wants to make at least one person happy. As such, he destroys his own statue to build a playground for the children of Cappy Town as he originally promised. Once he's finished, he immediately goes to Kirby's house and takes him there- as Kirby plays joyfully (Blissfully unaware of what's to come, which makes it even worse), Dedede finally accepts his fate. With that, he quietly joins Kirby on the swings and sings sadly to himself, crying Tears of Joy at having finally succeeded in what he set out to do-
Escargoon: You did it! You loveable lug, you finally listened to your heart for once!
[Dedede begins to tear up and walks past Escargoon, joining Kirby on the swing next to him]
Dedede:[Quietly singing] Swing away, swing away, save your cares for another day. Save 'em for another...day.
Heck, the dream Kirby has while trying to keep the egg dry can count. Kirby dreams he's floating in space when suddenly his mouth turns into a beak and his arms become wings. A bright light beckons him and he happily flies towards it. The empty space suddenly changes into bright lights as Kirby flaps his wings. Then he sees the egg sitting on a island stump under the leaf. He flies over to it and rests on top of it, like a real mother bird. He smiles and sighs before he rests peacefully, with his would-be child... He's so innocent. He doesn't even know if he really laid the egg or not and yet he's fully prepared to be a parent and do his best to raise his kid... The Japanese version adds to the scene with a beautiful, slow instrumental version of the "Kirby of the Stars" theme that really helps turn on the waterworks.