As I re-read The Lord of the Rings, I intend to also read critical essays and other commentary. 
rushthatspeaks recommended the first of these, the Le Guin essay I discuss below; I also borrowed from the local library Understanding The Lord of the Rings: The Best of Tolkien Criticism, edited by Rose A. Zimbardo and Neil D. Isaacs, which looked to have a good range of material. I have some meta essays at 
lotrfic_crit bookmarked for later reading as well; other recommendations are welcome. (I do have access to a college library via Chad, though I should note that my background in literary theory is not strong.)
(Oh, and I think I forgot to say this earlier, but there may be spoilers for everything Middle Earth in these posts. If you haven't read the books yet, these posts will not be safe for reading along with. Via kalimac, here's a blog with chapter-by-chapter posts during a first reading; The One Ring.com has a similar list of articles by "A Tolkien Virgin," but the site's down until July.)
Ursula K. Le Guin's essay "Rhythmic Pattern in The Lord of the Rings" was originally printed in the anthology Meditations on Middle Earth, edited by Karen Haber. The version I read, which has a short note written after the first of the movies, is in The Wave in the Mind, a collection of talks and essays by Le Guin. You can also find the text of the essay, with some odd typos, at the Lord of the Rings Fanatic Site; it is not clear to me whether it's up by permission or not.
Le Guin's thesis is simple:
The rhythm that shapes and directs his narrative is noticeable, was noticeable to me, because it is very strong and very simple, as simple as a rhythm can be: two beats. Stress, release. Inbreath, outbreath. A heartbeat. A walking gait—but on so vast a scale, so capable of endlessly complex and subtle variation, that it carries the whole enormous narrative straight through from beginning to end, from There to Back Again, without faltering. The fact is, we walk from the Shire to the Mountain of Doom with Frodo and Sam. One, two, left, right, on foot, all the way. And back.
She closely reads chapter 8 of Fellowship, "Fog on the Barrow Downs," and lists recurrent elements together with what they reverse into, "a pulsation back and forth between polarities of feeling, mood, image, emotion, action—examples of the stress/release pulse that I think is fundamental to the stucture of the book." Examples are "darkness/daylight," "confusion of thought/clarity," and "imprisonment or a trap/freedom"; later, she discusses the importance of directionality. After the list, she notes that "[t]hese reversals are not simple binary flips. The positive causes or grows from the negative state, and the negative from the position. Each yang contains its yin, each yin contains its yang. (I don't use the Chinese terms lightly; I believe they fit with Tolkien's conception of how the world works.)"
Le Guin then proceeds through the chapter, starting from Frodo going on ahead of the others, and discusses the events as they relate to this rhythmic pulse. She points of that after the pages of relief and relaxation when the hobbits are rescued, the plot is less tense, but the narration nevertheless draws the hobbits back into the larger, still-ominous plot that lies ahead.
The shadow of menace is inescapable. The chapter that began with a hopeful day-break vision of brightness ends in a tired evening gloom. These are the final sentences:
Darkness came down quickly, as they plodded slowly downhill and up again, until at last they saw lights twinkling some distance ahead.
Before them rose Bree-hill barring the way, a dark mass against misty stars; and under its western flank nestled a large village. Towards it they now hurried, desiring only to find a fire, and a door between them and the night.
These few lines of straightforward narrative description are full of rapid reversals: darkness/lights twinkling—downhill/up again—the rise of Bree-hill/the village under it (west of it)—a dark mass/misty stars—a fire/the night. They are like drumbeats. Reading the lines aloud I can't help thinking of a Beethoven finale, as in the Ninth Symphony: the absolute certainty and definition of crashing chord and silence, repeated, repeated again. Yet the tone is quiet, the language simple, and the emotions evoked are quiet, simple, common: a longing to end the day's journey, to be inside by the fire, out of the night.
After all, the whole trilogy ends on much the same note. From darkness into the firelight. "Well," Sam says, "I'm back."
Le Guin also points out that the barrow-wight foreshadows Sauron in its appearance and defeat. Thus, she concludes, the entire book depends on this pattern: "Relying on the irreducible simplicity of the trochaic beat, stress/unstress, Tolkien constructs an inexhaustibly complex, stable rhythmic pattern in imagined space and time. The tremendous landscape of Middle Earth, the psychological and moral universe of The Lord of the Rings, is built up by repetition, semirepetition, suggestion, foreshadowing, recollection, echo, and reversal. Through it the story goes forward at its steady, human gait. There, and back again."
Note: I decided to read this and then go back to Chapter 1, because the pacing of the entire opening is often criticized. Chapter 1 thus follows after dinner (and, possibly, a plea for fashion advice).