[Leyrana Silumiel]

I'd have to say this is my favorite part, from the chapter "The Steward and the King":

'What do you look for, Eowyn?' said Faramir.

'Does not the Black Gate lie yonder?' said she. 'And must he not now be come thither? It is seven days since he rode away.'

'Seven days,' said Faramir. 'But think not ill of me, if I say to you: they have brought me both a joy and a pain that I never thought to know. Joy to see you; but pain, because now the fear and doubt of this evil time are grown dark indeed. Eowyn, I would not have this world end now, or lose so soon what I have found.'

'Lose what you have found, lord?' she answered; but she looked at him gravely and her eyes were kind. 'I know not what in these days you have found that you could lose. But come, my friend, let us not speak of it! Let us not speak at all! I stand upon some dreadful brink, and it is utterly dark in the abyss before my feet, but whether there is any light behind me I cannot tell. For I cannot turn yet. I wait for some stroke of doom.'

'Yes, we wait for the stroke of doom,' said Faramir.

And then, on the next page...

And so they stood on the walls of the City of Gondor, and a great wind rose and blew, and their hair, raven and golden, streamed out mingling in the air. And the Shadow departed, and the Sun was unveiled, and light leaped forth; and the waters of Anduin shone like silver, and in all the houses of the City men sang for the joy that welled up in their hearts from what source they could not tell.

And before the Sun had fallen far from the noon out of the East there came a great Eagle flying, and he bore tidings beyond hope from the Lords of the West, crying:

Sing now, ye people of the Tower of Anor,
for the Realm of Sauron is ended for ever,
and the Dark Tower is thrown down.

Sing and rejoice, ye people of the Tower of Guard,
for your watch hath not been in vain,
and the Black Gate is broken,
and your King hath passed through,
and he is victorious.

Sing and be glad, all ye children of the West,
for your King shall come again,
and he shall dwell among you
all the days of your life.

And the Tree that was withered shall be renewed,
and he shall plant it in the high places,
and the City shall be blessed.

Sing all ye people!

And the people sang in all the ways of the City.

Those are just a couple of my favorites of all the scenes that made the biggest impressions. Several of my others have already been mentioned (like when Eomer found Eowyn on the battlefield and became furious, so he attacked the enemy with all he was worth).