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Tear Jerker: Tomb Raider 2013
Many times, though it's made worse if Lara is also crying.
The death of Roth and Grim given they go out saving Lara, and also Alex though it's played more for melancholy than tragedy.
When Lara kisses Alex on the cheek before running. Doubly so if you found his (more-or-less unmissable) journal entry that reveals his massive crush on her.
The first time Lara kills a man and the trauma she goes through.
Hell, pretty much everything Lara goes through. Of course, halfway through the game is around the point she stops putting up with the island's shit and starts paying it back everything it's dished out, but when that happens (particularly evident by the exchange she has with Reyes where she responds to a What the Hell, Hero? with a jaded acknowledgement that she's come to accept all the death happening around her as "normal") you'll want to hug her for differentreasons.
When you reach the Survivor's Beach section of the game, you'll find a document written by Jonas. It says how his father would go into fits of rage and how he and his brother used to have to hide from his wrath. During these times his brother would tell him of Pania of the Reef. He then states that his brother had returned to Pania, implying that he swam out to sea to drown. Jonas then goes on to say that if he's the last one left he'll go to Pania too.
More of a Fridge Tearjerker, but the Enemy Radio Chatter (if you hold off long enough to listen to it,) does a pretty good job of showing how a good number of the mooks you will wade through are reasonably ordinary people just trying to survive a hellish situation. Also, as you kill mooks you can occasionally hear another mook shout "Brother!" in horror as his comrade dies. It's somewhat ironic that most of the people she mows down are a lot more sympathetic than the first man she kills, even though he's the only one she seems to be traumatised by.