Wow. My "moment" is also when Ennis realizes there was "another fella." I nearly died the first time I saw that. It ripped my heart right out of my chest. Few among us have not felt that combination of pain, anger and nausea upon finding out there was someone else, and Heath captured it perfectly with subtle expression changes. I've honestly never seen an actor portray so much while not saying a word. The nuances in this scene alone should have won him the Oscar.
Also, when Cassie is tearing him a new one at the truckstop/diner (whatever it is) and he says "I'm sorry." Dear God. This was a totally broken man. You could tell at this moment that there was no fight left in him. He was done.
As someone else mentioned, the first goodbye. The hopeful, almost desperate look on Jack's face as he asks if Ennis will be back. A little OT, but every time someone I know says they're going to watch BBM for the first time, I always advise them to watch carefully, because there's one line about 40 minutes in that if you don't catch it (Ennis mentioning he left his shirt behind), you really won't get the last 15 minutes or so of the movie, let alone the end. And I still to this day believe that you don't fully "get" BBM until the third viewing. There's so much in it that doesn't whack you over the head--like the shirts--that it's nearly impossible to take it all in the first time.
Oh!! Jack's mother. When she says "you are welcome to go up there, if you want..." with a hand on his shoulder and a look of understanding and acceptance, and the way Ennis immediately picks up on it... his expression is so grateful and relieved, and as he silently acknowledges this unspoken pact, you can tell he knows there's a reason she's sending him up there. And as Ennis is standing at the door with her on the way out, the way he mouths "thank you for this" while gesturing down at the bag he's holding... again, I nearly died. Just amazing acting.