Not a line per se since the game didn't really have a real language, but when the older brother died in Brothers: Tale of Two Sons. I was sobbing hard. Even in the gibberish made up language you could feel the despair.
For me, it was a gameplay element. The point where you're swimming and have to use the older brother's stick just brought the whole thing together for me, and was something that could only be done within a video game, as opposed to any other form of media.