The flight over Los Angeles at the beginning while the battle is raging below. The sight of one of the biggest cities in the country getting torn to pieces, fires burning everywhere, smoke in the air, anti-aircraft fire blazing desperately into the sky.... The soundtrack at that point just hammers the horror and tragedy home.
The (completely inevitable, given the genre) death of Lieutenant Martinez.
One of the more powerful moments is when Nantz and Martinez are arguing, and Nantz starts screaming "No! No, no, lieutenant! No! NOT AGAIN!" Made even worse right afterward, where the rest of the Marines, not hearing what was said, assume Nantz left Martinez to die, per his reputation.
The part where Nantz recites the names and ranks of each and every one of his comrades who died under his command during the mission he is infamous for. The look on his face deteriorates as he goes down the list from stern to broke, and to see such a strong character (obviously ridden with guilt throughout the movie) finally break down...
Any member of any military organization who has ever had someone die under his or her command can sympathize with the indescribable guilt that Nantz feels.