This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Good, the Bad and the Ugly
The Confederate outpost Angel Eyes encounters in the extended cut of the movie. The terrible conditions the soldiers were left in were enough to have him feel sympathy for them, even as he's doing his job in looking for Bill Carson.
The scene where Confederate prisoners are forced to sing loudly to drown out the sounds of Wallace beating the crap out of Tuco. Many of the prisoners are visibly weeping, as they know exactly what's happening to Tuco inside the cabin, but they can't do anything to help the poor bastard. The lyrics to the song "Story Of A Soldier" make it even sadder:
Bugles are calling from prairie to shore, "Sign up" and "Fall In" and march off to war. Blue grass and cotton, burnt and forgotten All hope seems gone so soldier march on to die.
Bugles are calling from prairie to shore, "Sign up" and "Fall In" and march off to war. There in the distance a flag I can see, Scorched and in ribbons but whose can it be How ends the story, whose is the glory Ask if we dare, our comrades out there who sleep.
The scene where Blondie comforts the dying soldier with One Last Smoke and leaves him his jacket.
Tuco and his brother. It bring a lot of Alternative Character Interpretation to Tuco. He feels betrayed by Pablo and believes himself to be in the right for living the way he does. Then they start fighting, but pause for a moment, before Tuco runs off to join Blondie at the wagon. Pablo's crushed expression says it all; that he was willing to try and make it up to his brother but he was too late.
Tuco is thunderstruck by the death of his parents and grieves quietly for them after he receives the news.
Tuco trying to find the grave where the money is buried. He runs through the vast graveyard, trying to find one particular tombstone in a forest of tombstones to fallen soldiers slaughtered in a tragic war, as Ennio Morricone's "The Ecstasy Of Gold" works up towards a climax.
After getting fatally wounded in battle, through sheer force of will, Captain Clinton stays alive long enough to watch Blondie and Tuco blow up the Branstone Bridge he's been bitching about. When it happens he dies with a smile on his face.
Captain Clinton: Can you help me live a little more? I expect good news.
The music itself that plays in the scene ("Carriage Of The Spirits") is also worth a mention.
"I've never seen so many men wasted so badly."
The Captain is visibly in pain while fellow soldiers are operating on him. Even Tuco can't help but cast a pitying glance at him.
Poor Tuco back in the noose again during the final scene. After all he's been through, after we've gotten to know him, it hurts to see him like this, his broken cries of "Blondie!" echoing out over Sad Hill as Blondie rides off into the distance is heartbreaking. Of course Tuco is saved, and he was right, Blondie was playing a joke on him, but the buildup is painful because you're not sure whether he'll live or die.
Maria in her only scene in the entire film. A mistreated and bedraggled prostitute, thrown violently off a carriage full of drunken revellers, then, running straight into Angel Eyes' trap and getting struck repeatedly by him for information on where Carson is now.