Hoosier's last scene gets this troper every single time. The fact that the ONLY thing he says to Leckie after "I lost my fucking weapon," is this very tiny, barely audible "Sorry"...
Many of the Heroic BSOD moments, such as the ones depicting Marines home from the war as being very emotionally scared from their experiences. Sledge breaks down into tears while dove hunting with his father, and Basilone goes to a driving range and hammers golf balls all day until his hands bleed.
Sledge cradling a mortally wounded Okinawan woman in his arms and stroking her hair as she dies in part 9.
Knowing full well John's newlywed wife Lena Mae Riggi Basilone has become a widow at the end of Part 8.
They definitely put her crying on the beach where she and John fell in love at the end of the episode just to invoke this trope.
Not to mention the epilogue tells us she never remarried.
When you read and understand how much John really meant to her, it makes things that much more tragic: historically, she carried a picture of him in her wallet until the day she died, and when a friend asked why she never remarried, Lena's response was "Once you've had the best, you can't settle for less."
Captain Haldane's death is definitely one, especially when one reads Sledge's book and sees that he really was that honorable and beloved by his men.
When Snafu and Sledge are on the train home in Part 10, Sledge is asleep with they arrive at Snafu's stop. He gets up and leaves Sledge without waking him to say goodbye. Made much more heartbreaking when the epilogue reveals Snafu didn't contact him and other Marines for over 35 years after the war.
Sledge's post-war Heroic BSOD, where he weeps bitterly and apologizes to his father for having enlisted.
Captain Ack-Ack quietly saying "Eddie? Eddie?" when Hillbilly dies, as if he can't believe he's dead
Right after the scene with the Japanese soldier commiting suicide with a grenade, there's a scene with a surviving Japanese soldier which is being toyed with by the Marines as he has a nervous breakdown before finally getting a Mercy Kill from Leckie. The Japanese's cries of utter despair and sorrow as he gets shot are heartwrenching, and then the final nail in the coffin comes when a picture of him and his wife is shown, which shows that the people on both sides of the war are, in the end of the day, human beings who want to return alive to their beloved ones.
The fact that our last shot of Chuckler (who, spends most of the series smiling, laughing, and looking after his friends) is of him wounded and despondent, being carried away from the battlefield on a stretcher.