Seeing the Little Sister hug Sackboy in the intro. It's so adorable! Even if Daddy doesn't think so.
In the actual rivalry cutscene, Sackboy creates a hopscotch board (in his story) or a jump rope (in Big Daddy's story) for the Little Sister to play with. It's even more adorable with the jump rope scene as the two jump together. Awww...
Hell, the ending of Sackboy's story is full of sweetness. Stephen Fry's narration about Sackboy returning to his home and how he smiles when people use their imagination to create and share happiness is nothing short of beautiful.
Sackboy's intro is also heartwarming in itself. His reason for joining the fight? He heard of worlds where destruction outpaces creation, and wants to make them better with his creativity. Awwwwwww.
Sackboy is essentially a Crowning Character of Heartwarming.
Sir Dan saving Fat Princess then offering his sword in service. Sure, she walks away bored, but it's the thought that counts.
This video. A fan who played Toro and got top 16 at an event loved the game, but didn't have a PS3. After said fan promoted the game on Reddit and the official forums, in an act of appreciation, Super-Bot said they were going to send the fan a t-shirt. What was unexpected was Super-Bot gave him not only three t-shirts, but a free PS3 signed by the entire development team and free copies of Resistence 3, God of War 3 and Killzone 3.
When Heihachi's Level 3 Super is used on Jak and Daxter, you can see Jak alone bound to the rocket while Daxter struggles to pry the chains off his friend despite the action guaranteeing that he'll be launched into space too. The entire sequence almost makes you want to cheer Daxter on despite the futility of it all (Heihachi's Level 3 being a cinematic).
This thread. Meant to fill in for a player who said she(yes, she) was leaving the community, the player made it her last request for her finalmatches with Youtuber LIQUIDFGC to be uploaded. What really makes it Heartwarming crossing over into Tear Jerker is, despite LIQUID trying to provide commentary, you can't deny that there is an inherent sadness in his voice as he talks, making it seem like he's about to cry, which he admitted. Truly a wonderful farewell.