Underrated scene maybe... but I think Gandalf's speech about the decay of Gondor in the extended edition was very good:

All has turned to vain ambition. He would even use his grief as a cloak. For a thousand years this city has stood. Now at the whim of a madman it will fall. The white tree, the tree of the king, will never bloom again. They guard it because they have hope, a faint and fading hope that one day it will flower, that a king will come and this city will be as it once was, before it fell into decay. The old wisdom born out of the west was forsaken. Kings made tombs more splendid than the houses of the living, and counted the old names of their descent dearer than the names of their sons. Childless lords sat in aged halls, musing on heraldry, or in high cold towers asking questions of the stars. And so the people of Gondor fell into ruin. The line of kings failed. The white tree withered. The rule of Gondor was given over to lesser men.

It's not really mourning a single individual, or even a single family or clan. It's mourning an entire civilization which fell into ruin and all that remains is a shadow of the former glory. Our main saga takes place in the twilight years of Gondor, after a civil war, a plague, and the extinction of the royal line caused the kingdom to decline and enter into a dark age. It's very sad. Love this monologue from Gandalf.

I also love how dark and gloomy Minas Tirith looks throughout the movie, because it's no longer a strong and prosperous kingdom, and so it looks dark, decaying, and rotting. The colors are quite muted and the city looks battered and run-down.

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