MacGuffin: Frequently described as such although it doesn't really fit because it has powers which are crucial to the story, the Ring was originally intended to be a sequel hook to The Hobbit until Tolkien decided it was actually an Artifact of Doom.
Made of Indestructium: Quite possibly the origin of this trope. The only ways to destroy the One Ring are to "unmake" it at its place of creation or for a greater smith than Sauron destroy it (the Valar, who would have to break their own rules, or Fëanor, imprisoned in the halls of Mandos).
Gandalf muses that dragons can destroy ordinary Rings of Power, but no dragon currently living has the firepower to do the job on the One Ring, nor did even the greatest dragon of antiquity. Unspoken: it'd be really hard to find a dragon to ask, who would be willing to help.
The Magic Goes Away: Elves sail off to the West, wizards leave (or otherwise drop off the radar), no more magic. Tolkien was extremely loath to use the word "magic" to refer to any of that in the first place.
Magic Is a Monster Magnet: Putting the One Ring on your finger lights you right up on Mordor's radar. Also, Gandalf is hesistant to use his magic while traveling with the Fellowship for fear of attracting attention from both Mordor and Saruman.
Manly Tears: Crying appears acceptable in most Middle-earth societies, and there are many instances of manly men weeping, a point on which Tolkien significantly differs from the old sagas that inspired him.
When Éomer discovers Théoden has been killed, he improvises a verse (of course) where he says that they need to keep fighting, and there will be time for the women to weep later. But the narrator mentions that Éomer himself wept as he spoke.
In the second book, the orc Gorbag says to Shagrat:
But don't forget: our enemies don't love us any more than they love Him, and if they get topsides on Him, we're done too.
In the third book, after Frodo and Sam saw a little orc kill another of their own:
For a while the hobbits sat in silence. At length Sam stirred. "Well, I call that neat as neat," he said. "If this nice friendliness would spread about in Mordor, half our trouble would be over." "Quietly, Sam," Frodo whispered. "There may be others about. We have evidently had a very narrow escape, and the hunt was hotter on our tracks than we guessed. But that is the spirit of Mordor, Sam; and it has spread to every corner of it. Orcs have always behaved like that, or so all tales say, when they are on their own. But you can't get much hope out of it. They hate us far more, altogether and all the time. If those two had seen us, they would have dropped all their quarrel until we were dead."
Meaningful Name: Virtually all Tolkien's names, whatever language they are in, have a meaning, though sometimes this changed over the years as Tolkien's languages evolved. Characters also acquire names over their lives which reflect personal qualities or great deeds. See the trope page for more details.
Meaningful Rename: There's a number of times when people get names/titles added to them at are meaningful but a true example would be when Gandalf comes back as Gandalf the White. He's taking Saruman's place and doing what Saruman should have been doing when he went over to The Dark Side.
Medical Monarch: Aragorn is recognized as the true king of Gondor when he uses his medical knowledge (acquired as a Ranger) after the battle of Minas Tirith.
Medieval Stasis: And when they're not standing still, they're going backwards. Justified by the dwindling population of the West, and the steady procession of wars and plagues engineered by Sauron, but also by more metaphysical concerns. The grass really was greener in the Second Age, and the physical world less recalcitrant. As Morgoth slowly regains his power over the eons, matter is becoming ever more hostile to mind. (Yes, every time your shoe lace breaks, or your pen leaks, or your computer dies and takes all your information with it — or someone in your family gets cancer — it's Morgoth's fault. It wouldn't have happened in the Second Age; things, including human bodies, were more reliable back then.)
Many like to imagine the look on Sauron or Morgoth's face after seeing their armies crushed by artillery and bolt action rifles. Then again they'd probably just do what Sauron did to the Númenóreans, or reverse-engineer the technology if they didn't invent it in the first place; Sauron was a Maia of craft, and Morgoth was a Vala with similar leanings.
Initially, Tolkien did toy with the idea that Morgoth had more advanced technology. Drafts telling the Siege and Fall of Gondolin describe Morgoth's forces using crawling iron machines that sound suspiciously like the early tanks Tolkien had seen in World War One. (And in The Lost Road, Sauron ends up providing the Númenóreans with not only aircraft but the medieval equivalent of V-1 buzz bombs.)
Messianic Archetype: Several partial examples: Gandalf suffers a Jesus-like death to save his companions from a demonic threat complete with transfigured resurrection; Frodo's role as the defeater of evil by suffering a great evil; and of course Aragorn is the descendant of a fallen royal house, returning to reclaim his throne and restore his kingdom to glory. The former two fit the Christian notion of the Messiah, and the latter fits the Jewish version.
Mid-Season Upgrade: Gandalf suffers a Heroic RROD after killing only one Balrog. His bosses relax some of the restrictions on him to make sure that doesn't happen again.
The former city of Minas Ithil (the Tower of the Moon), renamed Minas Morgul (the Tower of Black Magic) after the Witch King took over. The river was poisoned, the flowers turned putrid, and the tower that was renowned for its white as the Moon beauty seemed instead as pale as a dead body, with a strange sickly luminescence over all.
The crossroads on the road to Minas Morgul was originally guarded by the statue of a former king. By the time Frodo and Sam pass that way, the statue's original head has been replaced with a rock painted as a grinning cyclops, presumably intended to represent Sauron.
The appendices mention that Sauron was quick to remove the pillar marking where the Numenoreans landed to capture him during the Second Age when Harad fell to his control.
Mooks: Rather a lot of them, actually effective when they aren't fighting one-man-battalions (like most of the main characters).
Mortality Ensues: In the end, Arwen gives up her immortality to be with Aragorn.
Multinational Team: The Fellowship, which brings together heroes from across Middle Earth.
The Musical: A rare (possibly unique) literary case. Expect any important event to inspire someone to improvise a song, or at least a poem. Among those listening, someone will often join in — especially if they're an Elf.
There is actually a musical adaptation of the story. Reactions to it are mixed.
A more minor example: Gríma Wormtongue. Appropriately, more creepy and insinuating then a direct threat.
Narrative Poem: Many. Among them are: "Eärendil was a Mariner" and an excerpt from the lay of Beren and Lúthien.
National Weapon: Axes for dwarves — the association is strong enough to make it into their standard battle-cry. Tolkien is probably also responsible for the standard fantasy association of bows with elves, though he doesn't really use it. Legolas habitually uses a bow, but fights with long knives when he runs out of arrows. And elves in general are just as likely to use swords or spears .
Near Villain Victory: Tolkien basically coined the word "eucatastrophe" to describe this trope; it happens plenty of times throughout the novel, being a particular favorite trope of his.
The Necrocracy: The kingdom of Angmar in the Back Story and Minas Morgul in the main story. Appropriate, as they're ruled by the same evil sorcerer.
Negated Moment of Awesome: The showdown between the Witch-King and Gandalf at the gates of Minas Tirith is cut very short by the arrival of Rohan.
Never Accepted in His Hometown: Frodo Baggins goes unappreciated back in the Shire. Sam, who could have ended up as an unsung, thankless hero, gets elected Mayor of the Shire, while the oblivious hobbits overlook Frodo's ordeals.
Nice Job Fixing It, Villain: Saruman sending the Uruk-Hai after the Fellowship so he can have the Ring for himself. True, Boromir gets killed and Merry and Pippin are captured, but it ends up causing the downfall of Saruman's plans, since the hobbits manage to escape into Fangorn and rouse the Ents against him. Also, since Aragorn, Legolas and Gimli chase after them, they're perfectly placed to meet up with Gandalf again and help Théoden and his people, which in turn leads to Rohan being in a condition to actually aid Gondor...
Sauron letting Gollum go instead of just killing him once he'd gotten all the information he could out of him. To clarify: without Gollum, Frodo and Sam would never have been able to get into Mordor without getting captured, and without Gollum the Ring could never have been destroyed. Sauron really kind of shot himself in the foot with that one.
The One Ring itself is of the standard Made of Diamond variety. The only thing that will destroy is to throw it back into the fires of Mount Doom where it was forged. The entire series then revolves around accomplishing this.
The Ringwraiths are incredibly difficult, though not impossible, to permanently destroy, and are immortal thanks to the powers of the nine magic rings that sustain them. The only ways to permanently destroy the Ringwraiths are to destroy their rings (which Sauron keeps in his personal possession) or the One Ring. In his letters, Tolkien says that Sauron could have restored the Witch King in time, if not for those meddling hobbits dropping his Ring into a volcano.
Word of God once mentioned that this case of the trope, as well as the whole idea of the Ents, was directly inspired by Macbeth. Tolkien said that, as a child, he had been disappointed that Macbeth wasn't just killed by a woman and that Birnam Wood didn't actually get up and march against Macbeth.
Non-Linear Character: Galadriel to an extent, which let her create her magic mirror. Some other elves with strong foresight can act like this too.
'I wish Merry was here,' he heard himself saying, and quick thoughts raced through his mind, even as he watched the enemy come charging to the assault. Well, well, now at any rate I understand poor Denethor a little better. We might die together, Merry and I, and since die we must, why not?
Nothing Is Scarier: Deliberately invoked by the author in the case of Sauron himself. Only three characters — Pippin and Aragorn, via the palantír of Orthanc, and Gollum, presumably during his Mordor torture — have actually seen Sauron's face, and none of them is inclined to describe him. The nearest we get to any physical description is Gollum mentioning the Black Hand, which only has four fingers after Isildur cut one of them off.
Also this bit, from Moria:
Gandalf: I do not like the feel of the middle way; and I do not like the smell of the left-hand way: there is foul air down there, or I am no guide.
The murk of Shelob's cave causes not simple darkness, but complete sensory deprivation except for the hideous stench.
Nothing is actually seen and nothing happens in the Paths of the Dead, but the dread of anticipation increases with each line on the pages until it becomes downright palpable. There's also the great door in the Paths that some poor soul had tried to open to his dying breath. We never find out what's behind it or why the man (Baldor, son of Brego) wanted to get in, but you can be sure that the question will haunt you for the rest of the chapter, and beyond.
Nude Nature Dance: After the hobbits have been extricated from the Barrows, Tom Bombadil removes the clothing the wights had placed on them and invites them to "run naked in the grass" while he retrieves their ponies. It's part of breaking the curses they were under, apparently, as was giving away the wight's treasure.
The Oath-Breaker: The Dead. Isildur cursed them such that their kingdom would die and they would never rest when they swore to help him fight and then broke their oath. Three thousand years later, they break the curse by helping Isildur's heir Aragorn.
The Obi-Wan: Gandalf, mentoring Aragorn, Frodo, and Faramir.
Obviously Evil: Sauron and most of his servants, though he used to be able to put on a fair face.
Offing the Offspring: Denethor, after he went into full-blown insanity and despair, tries to burn both himself and his feverish son Faramir alive on a pyre.
Oh Crap: Several of these, such as when the heroes are confronting the latest spawn of darkness (the Black Riders, the Balrog, the Witch-King, etc). The best, though, is when Frodo puts on the Ring at the very edge of the Crack of Doom: Sauron sees and senses Frodo, and it finally dawns on him just what his enemies are up to, how they tricked him, and how close they are to bringing about his utter ruin... and he is so terrified that he completely forgets there's a war going on right outside his gates. "And Barad-dûr trembled from the depths of its foundations to its proud and bitter crown."
Old Windbag: Many of Bilbo's neighbours and relatives seem to see him as this.
The Older Immortal: This often happens due to several long-lived and immortal races, from which the respective older ones either survive their peers or simply happen to live a among a different group whose members are younger and less powerful.
Older Is Better: The swords from Númenór are much better than their present day counterparts.
Elves, dwarves, hobbits and some men (Númenóreans and their descendants), mostly due to aging slower than the corresponding mortal men. Elves become adults at 50 and hobbits are regarded adults at 33. Dwarves have a similar system to hobbits, but live about twice as long (at 67 Gimli was considered too young to go on the quest of Erebor, but in the prime of his life at 139). Aragorn dies at 210 and Faramir at 120, which are reduced lifespans compared to their Númenórean ancestors, who regularly lived 300-400 years. There are quite a few elves in the story who have lived many thousands of years.
Bilbo and Frodo are a special case of this, since their youthful appearances ("well-preserved") are actually an effect of the Ring. It's considered outright bizarre by other hobbits that Bilbo, at the ripe age of 111, looks about fifty-five years old.
Out of the whole of the Fellowship, Boromir - and possibly Sam and Merry - are the only ones that actually look their age (to the reader's eyes at least). Pippin could be mistaken for a young (human) boy but is in his late twenties, Frodo is fifty but looks as if he's barely out of his tweens, Aragorn is eighty-seven, Gimli - as stated before - is a hundred and thirty nine, Legolas is at least five hundred years old, and Gandalf, as a Maiar, is older than the world itself.
The Omniscient: Galadriel and Sauron, particularly in Fellowship of the Ring. However, they can't see everywhere at once, and some beings like Gandalf can cloud their sight.
One-Gender Race: The Ents, although not by design as there originally was a distinct female gender - only they vanished, and haven't been seen since. If they did not have such long lifespans, they would be extinct already for lack of children. (The situation is elaborated upon in the trope entry).
One Sided Battle: The battle at the Black Gate was this until the Ring was destroyed. It was never expected that it would be won though, since it was a desperate gamble to buy Frodo more time.
One Steve Limit: Averted; the Appendices reveal that a number of significant names have been reused throughout history, including Beren, Aragorn, Denethor, and Boromir.
Orcus on His Throne: Tolkien does this with his villains, but only towards the ends of their careers - he had a theme of deliberate Villain Decay and Motive Decay, with smart people with real goals turning to evil but evil itself corrupting them and gradually turning them into cardboard cutouts. Together with this, they start out going out and kicking arse by themselves (e.g. Morgoth fights Tulkas personally at the dawn of time, Sauron comes out to fight Huan in the Silmarillion) but eventually becoming throne-bound. Often after one too many of such direct interaction had a painful outcome (e.g. Morgoth after his duel with the elven king Fingolfin, Sauron after his defeat/half-death and loss of the Ring in the War of the Last Alliance).
There's also the fact (according to "Morgoth's Ring"), that Melkor/Morgoth and Sauron spent much of their power controlling their "agents". They were not exactly lazy: using their physical incarnations to go into battle would have been simply foolish, especially for Morgoth, who "at the time of the War of the Jewels had become permanently incarnate" trying to control physical matter and who as a result could be killed in battle. For example, it's implied that the orcs' ferocity, tirelessness, and rage (along with their tendency to kill each other over nothing) come from being controlled and empowered by Sauron's will.
The last time Sauron personally took part in battle was at the end of the Second Age, during the Elves and Men's attack on Mordor, when he steps out of the tower and displays his badass powers, but ends up losing the One Ring, his ring finger, and his physical body.
Order Versus Chaos: This is played out in the race of Ents: male Ents loved the wilderness and forests, nature untamed, while the Entwives cultivated gardens and loved orchards and farmlands. The two genders drifted apart over the years, and the Ents have since lost the Entwives completely. Also could be described as nature vs civilization.
Our Angels Are Different: The Istari, the wizards, are angels disguised as Men, complete with the same aging process that Men endure; Saruman, for example, had black hair when he first arrived on Middle-earth, which gradually turned white over the millennia until only a few black hairs remained in the main story.
It's worth noting that Tolkien's orcs are actually quite different from the standard Chaotic Evil barbarian orcs when you look beyond the superficial level. They're actually a technologically advanced race (The Hobbit mentions that they are as a rule better craftsmen then dwarves if they take the trouble, which they usually don't) who are generally of human-level intelligence and have a sophisticated appreciation for others' pain. The problem is, they're usually not working together in large groups unless forced to do so by an outside force, and in fact kill each other at the drop of a hat if no other enemies present themselves. Frodo implies that their rage comes from the will of Sauron, who wants his servants ferocious and berserk. This brings in shades of Sanity Has Advantages.
Overly Long Name: The Ents, combined with the fact that they talk really, really slowly.
Add to that their immortality, their isolated civilization and how generally hard to kill they are. Keep in mind that an Ent's full name is essentially his entire personal history, and they are quite old.
Treebeard also implies that the full Entish name for Orcs is several years worth of insults strung together.