The true ending of Kirby 64 The Crystal Shards, shown on the right. Ribbon actually kisses Kirby. This then becomes a Funny Moment as Kirby gets so... erm... charmed that he dances around and falls down the stairs.
The Waddle Dees in Kirby's Epic Yarn seem like they would rather pal around with each other than get in the way. Try not to stop and smile at them playing catch or even just falling asleep where they stand.
In the post credits scene of Epic Yarn, Kirby is seen under sleeping under some trees, holding the magic sock.
In fact, playing any Kirby game, especially the old ones, qualify as a heartwarming moment because of the sheer amount of nostalgia fuel within them.
The part of Super Star where Meta Knight orders his followers to evacuate the Halberd. When they insist on staying to fight Kirby, he acts like he doesn't care what happens to them, and it sounds like he's trying to get them mad enough to leave so they won't get hurt. Then he apologizes under his breath, either for snapping at them, getting them in danger in the first place, or said faking of indifference towards their fate.
A minor one, but after the credits of Squeak Squad, we find out that the Squeaks sent Kirby's cake back as an apology for causing so much trouble. It's such a nice thing to do, especially after Kirby endlessly beat them all up just for that cake slice.
A more minor one, but in Kirby's Dream Collection, Magolor states that after the events of Return to Dreamland, he wanted to apologize to Kirby by building him a theme park. He actually means this, and that the only action that even closely resembles maliciousness is attacking you when you race.
It gets more heartwarming after remembering one of Magolor's quotes from Return to Dreamland. He thanks Kirby for helping him and hopes that they can be friends forever, which is originally implied just to be Magolor sucking up to Kirby to help him get the Master Crown. But Magolor's actions after returning prove that this wasn't a lie. After all, he DID say he was legitimately thankful for Kirby's help after getting the crown.
Heartwarming in Hindsight: Kirby Air Ride was the last game that Masahiro Sakurai was personally involved in before he left Nintendo to found his own company. At the time, there were rumors floating around that he considered Air Ride to be an Old Shame due to the amount of Executive Meddling involved during development. However, every project Sakurai has worked on since then has had at least one thing in common with Air Ride: Super Smash Bros. Brawl and Kid Icarus: Uprising borrowed the way that certain features were unlocked via a large grid that slowly revealed more objectives the more you unlocked, along with a tool to bypass certain objectives that the player found too challenging. Not to mention the concept of the Dragoon and the Hydra; a potentially game-breaking ability that's divided into three parts that players have to collect or fight over before it can be used. Not only did the Dragoon appear as an item in Brawl, but this is also how Daybreak works in Uprising's multiplayer mode. And finally, the Smash Run mode from Super Smash Bros. for Nintendo 3DS was explicitly stated during a Nintendo Direct to have been inspired by Air Ride's City Trial mode. Looks like Sakurai doesn't hate Air Ride after all!