In the movies it was Elrond's reaction when Aragorn and Arwen kissed. You've heard the saying "You're not losing a daughter; you're gaining a son"? In Elrond's case, he really was losing a daughter. Hugo Weaving nailed it with his half-laughing, half-crying expression as everyone else cheered.
I think it would be in the tower of Cirith Ungol when Sam, in dispair, starts singing to the part when he finds Frodo.
"Like a child at rest, when night-fears are driven away by some loved voice or hand."
On the battle fields of Pelennor when Theoden was saying his final farewell to Eowyn - "My eyes darken, my body is broken, you have to let me go! I go to my fathers in whose mighty company I shall now not feel ashamed!" Beautiful, stunning and so heartfelt - gets me every time!😭😭😍😍
Whenever I read the end of ROTK, I always get a little teared up