So, anything that touched your heart in some way. Whether it was sad, romantic, warmed your heart, made you particularly pissed off at a particular character/faction, whatever.
My first submission, and the moment that gave me the idea for this thread, is the last exchange between Veronica and McNamara during her companion quest.
It made me feel really bad for both Veronica and the Brotherhood. Just the way Veronica drops her snark and gets really soft and sad when she says "we'll die out." And he Elder responding with "I know." He feels like he has no choice but to let the Brotherhood waste away.