The game that's evoked the strongest emotions in me, by very, very far, is definitely Nier.
If you've played it and you're wondering why, that's because the developers of Nier are idiots and hid all the good bits in an alternate playthrough it never tells you about. After the credits roll the game starts again from halfway through, and things are... not particularly cheerful. Not that they were before, even the first playthrough was pretty sad at points, but yeah. Playthrough B is just heartbreaking. The game plays out the exact same way, but there are extra cutscenes in which you see things from a different perspective. And originally you couldn't understand what the enemies of the game were saying, but playthrough B adds subtitles that translate them. I can't really explain it in a way that people who haven't played the game would understand, so I won't go into detail. But seriously... wow. Playthrough B onwards of that game is just... wow. It didn't make me cry, but I did go quiet for a very, very long time after finishing it. And there were a lot of point where I didn't want to carry on because of what was going to happen.
But don't skip ahead and just play playthrough B if you somehow find a way to. You need to play playthrough A first to understand why it's such a kick in the nuts.
Big group hug to anyone who knows what I'm talking about.
(Honorable mention goes to Lost Odyssey. That game was pretty damn sad too. But it's got nothing on Nier.)