TL;DR You need to have a well-developed Character with a well-known set of Skills, who adheres to a certain Moral above all else. The reader must share the same Moral, or they will have no recourse to relate. The Moral must be put to the Ultimate Test, wherein the Character's Skill is shown to be at its Strongest, and Moral is at its Loudest.
Seems to me like all these examples are just a jarring use of slapping you in the face with the 'moral of the story' which has been worked up to all along.
<PERSON> fought so that his people could have Freedom. Screaming Freedom! at the precipice of ultimate change emotionally reinforces all that we have been working towards. It inspires everyone, giving the notion that 'This is it, this is what we have all been waiting for'
When <PERSON> has been so chivalrous and loving this whole time, and now he finally, willingly, pays the ultimate price for the love of his life, it speaks to the reader. It reinforces all the things we have previously known about <PERSON>, and washes everyone with remorse for <PERSON>'s beautiful, frozen soul.
When good-old <PERSON> inspires poor burdned <PERSON>, even at the Fringes of Middle Earth and on the literal edge of Doom, when all hope seems lost, (I'm getting chills just writing this) he is showing the audience his true colors, which they already knew about him. He is reinforcing our ideas about him, in the best way, by doing what he does best, in the clutch.
"Doing what they do best, when it counts" speaks for all of these scenarios, and many climactic moments, in general. 999
Whether its a wacky group of like-minded people, coming together to take down a larger-than-life opponent using their individual skills (Oceans 11), or a hyperintelligent detective consistently solving the crime (<PERSON>), we get a rush when people use their well-known skills to solve unorthodox or seemingly impossible problems.
It becomes a punch in the gut if misfortune befalls the actor, but they still solve the problem they set out to solve (<PERSON>). If they don't even solve the problem, that's pretty tragic, and if the character is crafted to be well-liked, the effect is more jarring than heart breaking. cough cough song of ice and fire
I'd say LoTR and Braveheart aren't so much gut-punching as heart-wrenching, but they all serve to draw a supreme level of empathy towards the actor. Because they all did what they do best, and their morals shone, to the extreme and in some cases to the end.
EDIT: I'd like to extend a nuance of this recipe, and in doing so give a shoutout to <PERSON> The Dark Tower Series.
! <PERSON> is known to love his surrogate son, <PERSON>. <PERSON> is also known to be responsible for <PERSON>'s deaths (multiple), in pursuit of his Ultimate Goal. The Betrayal seed as been set... And then <PERSON> dies for the final time.
additional spoilers in link
http://darktower.wikia.com/wiki/Jake's_Eulogy
It's utterly gut-punching, heart-wrenching, mind-quailing (to steal another <PERSON> phrase) all in one.
!I knew I shouldn't have expected anything else, but when it happened, and <PERSON> let his guard down ever so briefly to give us a glimpse into his terrible inner turmoil, and saw <PERSON> off with such love, remorse, loyalty, and compassion, it really tore me up.
It reinforced multiple things, <PERSON>'s drive towards the Ultimate Goal above all else, and the very tragic effect this had on his life. The juxtaposition of the two Morals existing at once, (pursuit and love, respectively), and the former consuming the latter, causing terrible grief.
I would wager that the more "layers" of a character you can make as raw as possible in the right moment, the more emotionally impacting the scene will be. 190