I have had the same favorite moment in this movie since the first time I saw it, a dozen years ago. In fact, it is my favorite moment in the entire trilogy. It makes me cry and cheer at the same time, and I cannot think right now of any other scene in any movie that affects me in quite the same way. No other moment that is that same blend of all that is triumphant and heroic and sacrificial and brave.
I am, of course, talking about this moment:
"I can't carry it, Mr. Frodo. But I can carry you!"
Just typing that line brings tears to my eyes. Samwise Gamgee, you're my hero.