I'll just give a handful, based on my present preferences (in six months' time you might get a different answer):
Book - FotR
1) I really loved the beginning of 'A Knife in the Dark' - Fatty Bolger's escaping the Riders.
2) But the best passage in the book for me (and one which as a teenager I've never appreciated), is the end if 'Lothlorien' - is Frodo's experience of the land:
The others cast themselves down upon the fragrant grass, but Frodo stood awhile still lost in wonder. It seemed to him that he had stepped through a high window that looked on a vanished world. A light was upon it for which his language had no name. All that he saw was shapely, but the shapes seemed at once clear cut, as if they had been first conceived and drawn at the uncovering of his eyes, and ancient as it they had endured for ever. He saw no colour but those he knew, gold and white and blue and green, but they were fresh and poignant, as if he had at that moment first perceived them and made for them names new and wonderful. In winter here no heart could mourn for summer or for spring. No blemish or sickness or deformity could be seen in anything that grew upon the earth. On the land of Lorien there was no stain...
Though he walked and breathed, and about him living leaves and flowers were stirred by the same cool wind as fanned his face, Frodo felt that he was in a timeless land that did not fade or change or fall into forgetfulness. When he had gone and passed again into the outer world, still Frodo the wanderer from the Shire would walk there, upon the grass among elanor and niphredil in fair Lothlórien.
And then his vision of Aragorn on Cerin Amroth.
Book - TTT
1) If I had to pick one chapter, it moght as well have been 'The Uruk-hai', because of the Ugluk-Grishnakh duel.
2) And if I had to pick a single sentence, in would have been Gandalf's from 'The White Rider', telling of his experience beyond the world:
Faint to my ears came the gathered rumour of all lands: the springing and the dying, the song and the weeping, and the slow everlasting groan of overburdened stone.
For one passage in TTT - there are two main candidates:
3) Frodo's sensing the Witch-king in the Morgul Vale, at the beginning of 'The Stairs of Cirith Ungol' - especially his heart going out to Faramir, and his being called by Sam:
Frodo stirred. And suddenly his heart went out to Faramir. 'The storm has burst at last,' he thought. 'This great array of spears and swords is going to Osgiliath. Will Faramir get across in time? He guessed it, but did he know the hour? And who can now hold the fords when the King of the Nine Riders comes? And other armies will come. I am too late. All is lost. I tarried on the way. All is lost. Even if my errand is performed, no one will ever know. There will be no one I can tell. It will be in vain.' Overcome with weakness he wept. And still the host of Morgul crossed the bridge.
Then at a great distance, as if it came out of memories of the Shire, some sunlit early morning, when the day called and doors were opening, he heard Sam's voice speaking. 'Wake up, Mr. Frodo! Wake up!' Had the voice added: 'Your breakfast is ready,' he would hardly have been surprised. Certainly Sam was urgent. 'Wake up, Mr. Frodo! They're gone,' he said. '...They're gone, and we'd better go too. There's something still alive in that place, something with eyes, or a seeing mind, if you take me; and the longer we stay in one spot, the sooner it will get on to us. Come on, Mr. Frodo!'
4) And the terrible counterpart to Lothlorien - the desolation before Mordor ('The Passing of the Marshes'):
...the lasting monument to the dark labour of its slaves that should endure when all their purposes were made void; a land defiled, diseased beyond all healing - unless the Great Sea should enter in and wash it with oblivion. 'I feel sick,' said Sam. Frodo did not speak.
Book - RotK
The great moments for me in RotK are moments of hope:
1) The star Sam saw above Mordor, in 'The Land of Shadow':
Sam struggled with his own weariness, and he took Frodo's hand; and there he sat silent till deep night fell. Then at last, to keep himself awake, he crawled from the hiding-place and looked out. The land seemed full of creaking and cracking and sly noises, but there was no sound of voice or foot. Far above the Ephel Dúath in the West the night-sky was still dim and pale. There, peeping among the cloud-wrack above a dark tower high up in the mountains, Sam saw a white star twinkle for a while. The beauty of it smote his heart, as he looked up out of the forsaken land, and hope returned to him. For like a shaft, clear and cold, the thought pierced him that in the end the Shadow was only a small and passing thing: there was light and high beauty for ever beyond its reach. His song in the tower had been defiance rather than hope; for then he was thinking of himself. Now, for a moment, his own fate, and even his master's, ceased to trouble him. He crawled back into the brambles and laid himself by Frodo's side, and putting away all fear he cast himself into a deep untroubled sleep.
2) The confrontation between Gandalf and the Witch-king at the Gate of Minas Tirith - especially with the cock crowing.
Gandalf did not move. And in that very moment, away behind in some courtyard of the City, a cock crowed. Shrill and clear he crowed, recking nothing of wizardry or war, welcoming only the morning that in the sky far above the shadows of death was coming with the dawn.
And as if in answer there came from far away another note. Horns, horns, horns. In dark Mindolluin's sides they dimly echoed. Great horns of the North wildly blowing. Rohan had come at last.
But as I've argued here, this scene works only if we see it as Gandalf staring in the face of utter defeat.
3) And possibly more than either, I like Faramir and Eowyn on the Walls of Minas Tirith, awaiting Doom:
'It reminds me of Númenor,' said Faramir, and wondered to hear himself speak.
...'Of Númenor? said Éowyn.
...'Yes,' said Faramir, 'of the land of Westernesse that foundered, and of the great dark wave climbing over the green lands and above the hills, and coming on, darkness inescapable. I often dream of it.'
...'Then you think that the Darkness is coming?' said Éowyn. 'Darkness Unescapable?' And suddenly she drew close to him.
...'No,' said Faramir, looking into her face. 'It was but a picture in the mind. I do not know what is happening. The reason of my waking mind tells me that great evil has befallen and we stand at the end of days. But my heart says nay; and all my limbs are light, and a hope and joy are come to me that no reason can deny. Éowyn, Éowyn, White Lady of Rohan, in this hour I do not believe that any darkness will endure!'
That's the books. And now for the Movies:
Movie - FotR
1) I felt the fall of Gandalf, and the last battle of Boromir, were done very well.
2) And I simply loved the portrayal of 'A Long-expected Party', probably because of Ian Holm; for instance, his speech was done brilliantly.
Movie - TTT
I think here I'll just pick one scene - the Rohirrim on the walls of Helm's Deep, watching the onset of Saruman's army. And especially one moment, for which I'll copy a previous post of mine:
Gimli at Helm's Deep, before the battle begins.
When he asks Legolas what's going on, the idiot elf thinks it's time to ridicule him about his height. But Gimli manages to laugh at it good-naturedly! Says a lot about his confidence in their friendship, and of knowing Legolas was just teasing (after all, Gimli has witnessed Legolas' break-down a few hours before).
I know many people have been greatly annoyed by what they saw as Gimli being the butt-end of comic relief. But for me, this part was worth everything. Would Thorin, or even Balin, be capable of this? I'm afraid not.
These two have great moments together in all the films - in FOTR it is Gimli telling Legolas about Galadriel's three strands of hair (was it in the theatrical cut? I don't remember), and in ROTK the "dying side by side with a friend" exchange. But this scene, about the actual dispelling of animosity, is the best.
By the way, you might find this whole thread interesting.
Movie - RotK
In this film I'll pick four examples, and expound only on the fourth:
1) Sam's carrying Frodo up Mt. Doom.
2) Theoden's telling Eowyn: "I would have you smile again". Yes, I know it's not in the book.
3) The best utterly fabricated scene - Gandalf and Pippin leaving for Minas Tirith, and Merry's reaction, going with Pippin to the stable, and then watching them go. One can't stay a purist after watching this.
4) Faramir's setting out for Osgiliath, and Gandalf's words to him.
Actually, the TE diminishes by far the effect of this scene - as they confrontation between Denethor and Faramir was cut.
In that scene, Faramir said the "Not if I found it by the highway..." line, but not as a "rash vow" (as Baldor made), but as a conscious decision based in understanding the Ring's evil. And in that scene, it was also Faramir who accosted his father with "You would not have known your son" - effectively destroying his own hero-image of Boromir.
After that, his leaving on the suicide mission to Osgiliath (and yes, it was wrong to portray it as such - but that's the issue of the movie's assassination of Denethor's character) is simply heartbreaking. The one scene which brings tears to my eyes.
Speaking of tears - the most heartbreaking passage in the legendarium, to me, is the first few pages of 'The Ruin of Doriath' in The Silmarillion, with Hurin's facing the utter ruin of his family and all his hopes, with his release being just another means for Morgoth to wreak his revenge on Elves and Men.
And my favourite passage in The Hobbit, is the end of 'A Warm Welcome':
So one day, although autumn was now getting far on, and winds were cold, and leaves were falling fast, three boats left Lake-town, laden with rowers, dwarves, Mr. Baggins, and many provisions. Horses and ponies had been sent around by circuitous paths to meet them at their appointed landing-place. The Master and his councillors bade them farewell from the great steps of the town-hall that went down to the lake. People sang on the quays and out of windows. The white oars dipped and splashed, and off they went north on the last stage of their long journey. The only person thoroughly unhappy was Bilbo.
Actuallly, this whole thread, in which others as well mentioned their favourite passages from The Hobbit, is worth reading.
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