The first is a scene with Matt Damon who plays Will Hunting, and Stellan Skarsgard who plays Gerald Lambeau, a mathematics professor who takes Will under his wing. One of the movie's plotlines is about how Sean Maguire (Robin Williams), his shrink, and Gerald Lambeau, both try to play a father figure in his life, in their own ways. Gerald believes that Will has great potential which he must actualize, and pushes him in that direction. Sean believes that Will first needs to learn how to trust, open himself up to the possibility of both love and hurt, and learn to be happy. The more obvious side to take is that of the shrink, so the more obvious ploy would've been to make the professor some kind of impersonal, pushy jerk. But the movie smartly sidesteps that ploy, and the way it does that is to add a simple five second postscript to an otherwise ordinary scene.
Will and Gerald are working on a proof on the board. It's mostly silent - the communication is through equations on the board. After a particularly nifty piece of math, they both sit back, satisfied, and look at what they've accomplished on the blackboard. And while they do that, Gerald reaches out and ruffles Will's hair. To me, that simple gesture is what humanizes Gerald beyond all measure.
Aside: You have to understand: ever since I read To Kill a Mockingbird, ruffling someone's hair has been, for me, the de facto expression of one's affection. So, while I find it a very significant moment, it might not be so for others.
The other great moment comes right at the end. In a scene that comes shortly before it, Will tells Chuckie how he doesn't see why he shouldn't be a bricklayer all his life. Chuckie's response to that is beautifully put:
Look, you're my best friend, so don't take this the wrong way. In twenty years, if you're still livin' here, comin' over to my house to watch the Patriots games, still workin' construction, I'll fuckin' kill you. That's not a threat. Now, that's a fact. I'll fuckin' kill you.A little later in the same scene, he says:
Every day I come by your house and I pick you up. And we go out. We have a few drinks, and a few laughs, and it's great. But you know what the best part of my day is? For about ten seconds, from when I pull up to the curb and when I get to your door, cause I think, maybe I'll get up there and I'll knock on the door and you won't be there. No goodbye. No see you later. No nothing. You just left. I don't know much, but I know that.It sets things up for the last scene, when Will finally gets his act together and goes off to California, and see if he could maybe win Skylar back. And Chuckie finds out about it the way he wanted to: he goes to Will's house one morning and knocks on the door, and he isn't there. No goodbye. No see you later. No nothing. The camera just stays on Ben Affleck's face for a few seconds, as he processes this, realizes that his friend is gone, and celebrates and mourns it in equal measure. The movie gives these two people enough time together to build up to this moment; this is a fitting payoff, and well-earned.