Well, that is a tough one. And there's a few of them. I'm going to bold the titles so if you see a title that you've not finished, obviously there's spoilers.
Bioshock: Infinite definitely gets a mention here, how can it not. I loved the original Bioshock ending too but the ending of Infinite raised it, in my eyes, from a pretty good, refined shooter with a really interesting, if quite odd and confusing, storyline, to it being the epitome of story-telling in a videogame. Everything suddenly made sense watching that ending, all those little things that seemed like nothing all just came together in such a perfect way, and it was all so obvious looking back! I sat back and just thought about stuff for like a half an hour and then talked to friends all about it for the rest of the night. For the rest of the week, even. Absolutely brilliant, definitely the deepest ending of any game I've played. And I loved the characters too, I loved how much emotion Elizabeth conveyed.
Another favourite of mine would be Final Fantasy: Crisis Core's ending. Definitely a tear-jerker, and I knew it was going to happen, but the game really made me care about the characters, especially Zack. He was such a refreshing character beside the typical Final Fantasy characters too, and it was a really lovely ending. It upset me but I definitely didn't hate it, was a really emotional, lovely end to a great story.
Finally, it's gotta be The Walking Dead's ending finale, really. By the end of that game, I cared so much about Lee and Clementine, and since I'd made all the decisions and everything I was really invested and immersed into everything. And every decision was pretty much with Clementine's best interests at heart, keeping her close to Lee. And so, watching that ending... never cried so much. After all 5 episodes watching the finale unfurl just tugged on my heart-strings so much, it was such an emotional experience and an amazing performance by Lee and Clementine. Watching her in tears not knowing what to do and Lee struggling to keep helping her, it was just, such a sad ending and yet it was really incredible. It's funny because it was definitely a game that touched me, I did genuinely care about Lee and Clem. Kudos, TellTale.
Also, I'll give a mention to Call of Duty: Modern Warfare 2. Most people will disregard COD's campaign and just write them off instantly but I quite enjoyed the stories behind them, and both MW1 and MW2 had some great moments. But, specifically, MW2's ending. What happened to Ghost, who I really liked, just came out of nowhere, and I really did like the ending. I thought it was a bit held back by the engine, I imagine that type of very immersive, first-person ending would have benefited from some better graphics, but, definitely didn't ruin it. Really enjoyed that campaign.
And that's really it.