In Wind Waker, Link's grandmother gets sick and delirious in the first half of the story. When you get back, she's begging you and your sister not to leave "your poor grandma all alone." If you cure her with a fairy note and really, why wouldn't you try?!, she gives a real tear jerker of a speech about how she'll try to be strong.
What makes it even sweeter is that it's a rare moment of Link having someone else show parental love for him. After so many games of him being pretty much alone to go risk his life in monster-infested dungeons and temples, how many times has he had someone say "I should be the one taking care of you"?
Even the practical, non-emotional reward for doing this is rather heartwarming: after you get Grandma all better, she whips you up a batch of your favorite home-made soup! (The fact that this is 2 helpings of the game's ultimate healing item simply makes this a Karmic Jackpot, and a just reward for your kindness.)
The entire ending of Wind Waker: from the King's Heroic Sacrifice, Hyrule's destruction, and finally Link setting off with the Pirates to find a new land everything fills you with a sense of hope for the future.
King: I have scattered the seeds... of the future...
Pretty much any scene with both Link and Tetra in it can be enough to make any gamer's stone heart turn all mushy...
The whole final fight. You were not fighting for Hyrule: all that was being destroyed around you. The only thing you were doing was fighting for your own lives so you could go find a new land.
Don't forget the moment when you finally rescue poor Makar from the Forbidden Forest.
How much Link cares for his little sister Aryll is really touching. Even the his facial expression and little laugh when he finally reaches Aryll in the cage is enough to make you all tingly.
The statue of the Hero of Time and the images of the 6 Sages in stained glass really drive home the awe and reverence that the people of Hyrule had for the people who had sacrificed so much, including their lives, to ensure that the kingdom was safe. It's nice to know that, with the Continuity Snarl that exists among the games at times, that at least once the actions of Link and his allies was remembered and honored.
I personally found many of the interactions with Medli just adorable. One particular moment in the Earth Temple made my heart melt:
Medli: I hope you're not offended by my suggestions. I just want to be helpful...