Cremia and Romani.
Nothing in any video game ever has really hit me like Cremia and Romani's story. I think, perhaps, it's because I am an older sister as well, and I understand Cremia's struggle to protect her sibling. I didn't even know about it until after Did You Know Gaming talked about it... and ever since then, I've always felt it was one of the most tragic moments in the series.
It's not so much the part with the aliens, but rather what happens after you help Romani protect the ranch. Romani is so cheerful, happy, and naive, not understanding that the moon is going to kill them. But Cremia is clearly distressed and begins to realize that they were in danger. Her conversation on the cart just shows how sad she is -- her best friend is marrying someone she loves, the moon is getting bigger, and her milk is being attacked by bandits. And all the while, she has to protecr her sibling.
Cremia ultimately decides to give Romani some Chateau Romani, a drink only for adults that Romani has clearly been wanting to taste for a long time. She's either trying to give Romani the happiest day of her life, or perhaps even dull her senses with the drink's effects. And Romani is overjoyed at this sentiment, while Cremia is holding back despair. It's so sad. And then, the last time you see them before the moon is going to crash is when they are both walking back to their house, and they both say "See you tomorrow." Romani says it excitedly, but Cremia says it hesitantly, knowing that there most likely will not BE a tomorrow.
That, my fellow Zelda fans, is horrifyingly sad. I cried. I've never cried at anything else in any video game except for this. Romani's obliviousness and her sister's halfhearted attempts to protect that obliviousness are just... ugh. Amazing. I even wrote a fanfic about this scene because I love it so much. It's so great when a story in any medium can make you feel simultaneously so happy and so sad for the characters.
Also, I disagree as well that MM is the only game to bring out so many emotions. LA, in particular, is another extremely clever and emotional game. I do think MM does it the most effectively, though. After all, I just finished explaining that this is the only game to make me cry. :p