Agree with the Cagney scene in angels with dirty Faces. Saw it as a 8-10 year old and it left me empty for weeks. Same with Cooper doing Gehrigs farewell speech.
If you have never seen Galipolli there are at least 2 scenes in there that leave your heart in your throat!
It was mentioned already, but this immediately jumped into my mind.
Schindler's List-- Schindler overcome with grief that he could have done more.
https://www.youtube.com/watch?v=vOoWpTxKJGA
Also, the Final scene in Cinema Paradiso:
https://www.youtube.com/watch?v=XFZqrcqKGhY
And, for me the scene in Field of Dreams where Cansella meets his father as a young man and plays catch.
For me it's a tie between two:
1. The fart scene in Stepbrothers really personified what a fart should be.
2. The Shrim Bath scene in Tim and Erics Billion Dollar Movie.
Herb Brooks speech at the end of "Miracle"