Heartwarming / Metal Gear Solid 2: Sons of Liberty
Snake's and Otacon's special handshake and hug after the death of Emma; it showed that Snake did care for Otacon far better than any words could.
Also the way that Snake tries to snap Otacon out of his grief by emphasising his place in the mission - while it might sound rather cold of him, he does this in such a way that makes it very clear how important Otacon is to him, to the extent that he knows he can't function in missions like this without Otacon's aid. And while it doesn't last for very long, it does actually work in making Otacon feel a bit better about the whole situation.
A bit more Heartwarming in the Japanese version, but still as much a Tearjerker: The pet parrot that Otacon removes from its cage after Emma's death says "big bro"/"onii-chan", "big bro Hal"/"Hal onii-chan", and "I want to see you/I miss you", indicating that despite the unhappiness between the two of them, Emma still loved Otacon as her older brother.
Snake using Gray Fox's last words from the previous game to inspire Raiden. Not only is Snake passing on his mentor's views to his new protege, but it also highlights just how much his life has changed since Shadow Moses incident - far from the self-described "hired killer" from Metal Gear Solid, Snake has grown into a man who fights for what he believes in rather than what he's told to do.
In a meta sense, the speeches Snake gives to Raiden at the end, as well as the post-credits speech, feels like Snake being kind to the player for once. The whole game can be seen as a scathing commentary on the fanbase and on video gamers as a whole, using Raiden as an audience stand-in...but in the end, there's potential good in all of us, and Snake's speech in that sense is incredibly uplifting. We can all make the world a better place and we can all leave behind some good things - yes, even you.
For the rare few who didn't despise Rose and all her dialogue, there are some incredibly sweet moments between her and Raiden, and the ending where they reconcile and promise to see the other for who they really are, while discussing how they're going to parent their child can still be heartwarming to some.