I'm going to put three, and they're all from
Lord of the Rings (though the most memorable part of
The Hobbit movies for me was when Bilbo spared Gollum):
1. The Charge of the Rohirrim at the Battle of Pelennor Fields. You can just see in their eyes that they have no hope of coming back as they charge across the field, and the Rohan theme playing and then the orcs start firing and it really gets me every time I watch
Return of the King.
2. this one is in the extended edition, but it still counts. the Journey to the Crossroads in
Return of the King, where Frodo and Sam see the statue-head of the King of Gondor crowned with flowers. it always stood for me as a sign that, no matter how bad things get, there is always hope.
3. not as profound as the others, but admit it, we've all been guilty of this one: Galadriel's unnecessarily scary scene in
Fellowship of the Ring. more than once it woke me up and demanded attention like a ghost in the room. i never fall asleep watching
Lord of the Rings afterwards.