Georg confronting Rolf, buying time for his family to escape. And then walking forward and taking the gun out of his hand.
The dinner scene. Despite all the nasty tricks they've played on her - including putting a pine cone on her chair - Maria kindly and near effortlessly shames the children into tears at how badly they've treated her. Captain von Trapp, surrounded by bawling kids and rather taken back, has this to say:
Captain von Trapp: Fraulein, is it to be at every meal, or merely at dinnertime, that you intend on leading us all through this rare and wonderful new world of... indigestion?
Maria (after sipping her soup and looking around calmly at the sobbing children):...Oh they're all right, captain; they're just happy.
On stage at the festival, Max openly gives the details of the Nazis' upcoming attempt to pressgang the Captain into the navy. They go right for him when the family disappears and you know it probably doesn't end well for him, but that's some bravery.
Captain von Trapp's defiant rendition of "Edelweiss" in the face of Nazis who probably wouldn't have been too pleased that the Austrians were being reminded that they weren't technically Austria anymore (and woudn't be for almost 10 years). His choking up midsong and Maria's taking over to lead him into a duet may also qualify as a Crowning Moment of Heartwarming as well.
Furthermore, one of the Nazi commandants is shown singing too, revealing that he cares more for Austria than the Reich.
The family singing "So Long, Farewell, auf Wiedersehen, Goodbye" as they literally vanish under the noses of the Nazis sent to take the Captain to Bremerhaven qualifies.
Doubly awesome because of how effortlessly they just sauntered out of the building, and they were telling the Nazis they were fleeing the country nearly the entire time!
Climb Every Mountain is generally considered this for the Abbess, and can also qualify as a Tear Jerker.