As the resident Zeldaphile, I have to post two moments from the Zelda series that I LOVE. Surprisingly, neither of them are from my favorite or "everybody's" favorite. SPOILERS APLENTY.
The first is from Wind Waker, at the end. Link makes his way to Ganondorf, and Zelda's there all sleeping and then Gannie goes into his Obligatory Final Boss Speechâ„¢. He goes on about how Hyrule got to be the way it is, and says, "Don't you see? All of you...
Your gods destroyed you!"
It's a very awesome moment, and in the final final battle, Link makes a great "WTF?!" face.
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The second is from Majora's Mask. The most involved (and arguably best) sidequest of the game is the Anju-Kafei sequence. You need all three days to do this, but you help a lot of people and get a couple of masks. At the very end, when Anju and Kafei are finally reunited in Stock Pot Inn, with an HOUR to go before the moon crashes, they kneel on the floor, hugging each other, and staring at Link. They're about to die and all that matters is that they've finally found each other. Link has (almost) no choice, but to leave them, go back in time three days and pretend it never happened. It's sadder than not reuniting them to begin with; it was the first and only Zelda moment to ever make me cry.