Pair the Spares: Tolkien originally wrote Éowyn as the love-interest for Aragorn, before he revised the story to include Arwen; therefore after he did so, Éowyn becomes rather hastily paired with Faramir, and a chapter is dedicated to their growing relationship.
Pals with Jesus: Frodo may just be a normal hobbit, but he has little difficulty in befriending the incarnate soldier of the Valar gods, Gandalf the Grey.
Panacea: The Athelas plant, with the right usage, though the exact extent of its healing properties is never explored.
Morgoth in the backstory was the greatest of the Ainur (angels) and ultimately becomes Satan.
Saruman, respected leader of the wizards and the White Council, winds up attempting to capture the Ring for himself and replace Sauron as Dark Lord.
Parental Favoritism: Boromir (the elder son) is heavily preferred to Faramir by their father, Denethor. It's especially emphasized in The Movies, where Denethor is shown as blatantly unfair; in the book, Gandalf at least believes that it is partly that Denethor is still grief-stricken over the death of their mother.
Parental Marriage Veto: When Elrond finds out that Aragorn and Arwen are in love, he sets down what seems to be a impossible set of restrictions on their marriage (Sauron must be vanquished, Aragorn must unite the ancient kingdoms of Gondor and Arnor and become High King once again). Needless to say, Aragorn helps fulfill every single one of these conditions, and Love Conquers All.
It also harkens back to The Silmarillion when Thingol tasked Beren with retrieving a Silmaril from Morgoth's crown before marrying Lúthien (a task that Sam Gamgee openly recognizes as 'a darker danger' than their quest). Since Aragorn and Arwen are both descendants of Beren and Lúthien it seems appropriate; at least to Elrond.
Party of Representatives: Invoked at the Council of Elrond which calls for the Fellowship of the Ring to be composed of representatives from all free peoples of Middle-Earth.
Passing the Torch: Bilbo to Frodo, although not without one last attempt by the elder Mr. Baggins to join the new adventure.
The Password Is Always "Swordfish": The password to open the doors of Khazad-dum was written on the doors themselves. Justified in that it wasn't intended to be a password in that sense, since the Elves of Hollin and the Dwarves of Khazad-dum were close allies.
Past Victim Showcase: What the Mouth of Sauron hints at when he shows Frodo's mithril shirt, his elven cloak, and Sam's sword (which Sam had switched with him when he presumed the other hobbit dead) to the Captains of the West at the Black Gate.
Pet the Dog: Gollum has a rare moment of humanity when he catches Frodo and Sam asleep on the stairs of Cirith Ungol. He even attempts to pet Frodo's knee. Unfortunately, the moment doesn't last.
Phosphor-Essence: As Frodo succumbs to the Nazgûl blade, he perceives Glorfindel as "a shining figure of white light". Sam notes that, at times, it seems as if a light is shining through Frodo.
Pirates: The Corsairs of Umbar live across the sea south of Gondor and attack ships in the vicinity. ("Corsair" was a historical name given to Barbary pirates in the Mediterranean in real life, who may be the inspiration for them.)
Gandalf, servant of the Secret Fire and wielder of the Flame of Anor (which may or may not have to do with bearing Narya, the Elven Ring "red as fire"). However, he needs wood to sustain a fire, as he cannot burn snow.
In the battle that cost him the Ring, Sauron's body was described as blackened from the immense heat he gave off and even set people who got too close to him on fire.
Please Wake Up: Sam is left sobbing and desperately shaking his master from sleep after said master is stung by the venom of an eldritch arachnid. After some time, he mistakes sleep for death and leaves him to be taken by Orcs.
Plunder: After the Ents destroy Orthanc, Merry and Pippin collect a fine meal and pipeweed for themselves from the wreckage.
Points of Light Setting: By the time of the War of the Ring, millennia of war and social decline have left Middle-Earth in this state.
The elves and dwarves are Dying Races, the former restricted to four city-states often little more than fortified households and the latter a Vestigial Empire clinging on to life in a handful of far-flung outposts after the center of their civilization was lost to orcs, dragons, and worse.
The human kingdoms have been in decline for centuries or more, with the northern land of Eriador so completely destroyed by civil war and a great plague that the western Middle-Earth is almost totally devoid of human life, with only ruins and haunted cairnlands marking the old kingdoms' extent.
Outside of pockets of civilization and a couple of dying kingdoms, Middle-Earth consists of miles and miles of empty lands, dark forests where no one dares to go, ruined dwarf-cities crawling with monsters and lands ruled by orcs and human barbarians hostile to all outsiders.
The remaining holdouts of civilization are often highly isolated and superstitious — the hobbits have little to no knowledge of anything outside the Shire, for instance, while the Rohirrim have come to regard the elves of Lothlórien, one of the greatest remaining bastions of good, as malevolent fey ruled by a dangerous witch.
Poisoned Weapons: The Witch-King stabs Frodo with a Morgul-blade. If Elrond hadn't cured him, the poison of the blade would have turned him into a wraith. It's also mentioned in the books that orcs sometimes put poison on their blades.
The Fellowship of the Ring. When Frodo sits in the seat at the top of Amon Hen while wearing the One Ring, he sees many things with the seat's scrying ability, including Sauron's dark tower. Unfortunately Sauron detects him, and sends his will to locate him. Frodo barely manages to take off the Ring in time and Sauron's attack (in the form of a black shadowy arm) misses him.
LotR's "fancy crystal balls" are called Palantíri, and the problem with using them is that Sauron possesses one and can turn his will against anyone who tries using the others, with varying results:
Pippin gets away with nothing more than a terrible fright, but only because Sauron believes Saruman will send Pippin to him and is saving the real horror for an in-person interrogation.
Aragorn is (barely) strong enough to resist, and actually manages to wrest control of the palantír away from Sauron, but he is visibly shaken from the effort afterward. It goes both ways: the experience unnerves Sauron enough to accelerate his timetable.
Sauron is unable to corrupt Denethor to evil the way he does Saruman, but by forcing him to see only the might of Sauron's armies, drives him to despair and ultimately madness.
High Fantasy: It popularized the genre and is generally credited with creating it, although high fantasy in the novel format is actually older than Tolkien. The demand for novels similar to Lord of the Rings was so great that many imitators joined in to feed the demand. The term "Tolkienesque" has been used to describe the literature of his many imitators. A few writers actually tried to go in a different direction than Tolkien, such as Ursula K. Le Guin with her Earthsea novels. Even today, Tolkien's shadow is so big that it's difficult for a writer to escape it.
Hippies: The slang term "weed" sprang from a certain common misconception / bit of Fanon concerning Hobbit horticultural habits (Jossed by Tolkien himself).
Role Playing Games: The Fellowship can be seen as the prototypical RPG party. It established many archetypes and tropes that are seen RPGs like "rangers", warrior dwarves, the Balrog and Mithril. The Fellowship's trek through the dwarven city of Khazad-dûm might have been the basis for Ruins for Ruins' Sake. It inspired D&D and many of the RPGs that came after it.
War Gaming: Before LotR, war games were limited to historical wars like WWII, the Napoleonic Wars, and the American Civil War. LotR popularized the idea that war gaming can take place in a fictional land with fictional races and nations. It influenced such games as Warhammer, Warcraft, and StarCraft. Which came full circle when Games Workshop made a tabletop wargame based on LOTR, inspired partly by Warhammer.
Possession Implies Mastery: Subverted. About the only thing you get through mere possession of a great ring is invisibility. It may not even be possible for most ordinary beings to master. When Frodo wonders why he can't use the One to see the nineteen lesser Rings, Galadriel cautions him not to try.
Post-Climax Confrontation: The One Ring has been destroyed along with Sauron and the armies of Mordor, Aragorn has been crowned the king of Gondor, and the members of the Fellowship have separated to return to their homelands. When the hobbits return to The Shire, however, they discover it has been taken control of by Saruman, and they have to fight one last battle against him.
Post-Victory Collapse: Merry and Éowyn after defeating the Witch-King, Sam after defeating Shelob, and Frodo and Sam when they finally achieve their goal (though they do manage to make it down the mountain first).
Pre-Insanity Reveal: Gollum is a prime example. Originally a hobbit named Sméagol, he was corrupted mentally and physically by the Ring by the time Bilbo meets him in The Hobbit.
Produce Pelting: When Bill Ferny insults Strider and the hobbits as they walk out of Bree, Sam whirls on him and smacks him in the nose with an apple (which he regrets afterward, because it was a good apple).
Prohibited Hero Saves the Day: A major overarching theme. The hobbits are frequently encouraged to return to the Shire and let others take responsibility for the Ring, especially Pippin, the youngest of the group. All four of them prove to be vital to the quest in different ways. The same goes for Eowyn. As the highest-ranking female in Rohan, she's left behind to take care of Edoras while the men march to war, but comes along in disguise and manages to defeat the Witch-King, who could not have been beaten by a man.
Promotion, Not Punishment: During the siege of Minas Tirith, Beregond deserted his post and killed the porter with the keys to the Silent Street, as well as two members of the Guard. However, he only did this to protect Faramir from a premature funeral pyre, and only slew the others because they would not listen to him and attempted to kill him first. After the crowning of King Elessar, Beregond is brought before the new King. King Elessar spares him from execution because of the circumstances, but discharges Beregond from the Guard and orders him out of Minas Tirith... so that he may be reassigned to Faramir's newly-formed personal Guard in Ithilien as its captain.
Prophecy Twist: The Witch-King feels confident of his complete safety on the battlefield due to a prophecy stating he cannot be felled by any man. Then he runs into a halfling and a warrior woman on the field of battle.
Denethor sees the coming of the Black Fleet in the Palantír, and loses hope for Gondor defending itself against the onslaught from Mordor. Aragorn saw the same and went on to commandeer said ships, fill them with the now-unoccupied soldiers from southern Gondor, and helps turning the tide in Gondor's favor.
The Palantír does this a lot. Among other things, it also tricks Sauron into attacking Aragorn.
It's heavily implied that the Palantír also shows Denethor that Frodo is imprisoned in the tower of Cirith Ungol, leading him to believe that the Enemy has the Ring. He doesn't realize that Sam had taken the Ring, and is still free.
Even the elves get in on this. Glorfindel foresees that the Witch-King will fall "not by the hand of man," without mentioning that he will fall by the hands of a woman and a hobbit.
Word of God claimed that the last was inspired by Macbeth: Tolkien always thought that the quibble about Macduff not being "a man of woman born" was too inelegant, and it would have been much more satisfying if Macbeth had simply been killed by a woman. Similarly, the Last March of the Ents comes from Tolkien's disappointment that Birnham Wood didn't literally march on Macbeth's castle.
Merry and Pippin are downplayed examples. Tooks and Brandybucks have a reputation among other Hobbits for being more adventurous and warlike as Hobbit clans go, but Merry and Pippin just act like Hobbits. At least at first. Later both kind of go native and become something like Hobbit Swashbucklers.
The Rohirrim are a nation of barbarian warriors in the mold of Migration-era Germanic tribesmen like the Geats in Beowulf.
The Uruk-hai (pardon, the fighting Uruk-hai) boast about their battle prowess and ability to withstand sunlight. Their contrast with the Misty Mountain orcs couldn't be stronger.
Psychic Dreams for Everyone: Boromir's and Faramir's recurring dream about Isildur's bane that prompts Boromir to go to Rivendell. Frodo also sees Gandalf's escape from Orthanc in a dream, though he doesn't understand what he saw until he hears Gandalf's story later.
Psychic Powers: At the time the books were written, 'psychic' powers weren't indissolubly linked to sci-fi yet. Elves and Istari show various abilities. Aragorn, unsurprisingly, is The Ace in this area too: he foretells the future accurately several times, demonstrates supernatural healing abilities, and has the necessary mental strength to wrest the palantir from Sauron's control. Some instances, such as silencing the Mouth of Sauron, are more questionable.
The Quest: Frodo's quest is a double subversion. So much so, it might called an Anti Quest.
Quest to the West: The story inverts this as the heroes journey east and then south. Probably symbolic of the fact that they, in contrast to the vast majority of epic stories, set out to get rid of something rather than to find something. At the very end of the book though most of the characters do in fact travel all the way west - to either spend the rest of their eternal life there, or to die there.
Rags to Royalty: Aragorn, sort of. He was already the leader of the remaining Dúnedain in the north, but they collectively appeared to be this to most other humans. Among the elves, however, he and his people still had fairly high status. And when his father died early in his life, he was taken in and raised by one of the most important elven leaders still in Middle-Earth.
Ransacked Room: Happens to Frodo's house in Crickhollow after he leaves, as well as the Hobbits' abandoned room in the Prancing Pony.
Raven Hair, Ivory Skin: Luthien in the backstory and Arwen in the main story. Saruman also originally had black hair before old age turned most of it white.
"Ray of Hope" Ending: Although Frodo and Sam are parted at the end of the book, the appendices imply there is a chance they will be reunited one day in the West.
Aragorn is 87 and still going strong, Gandalf is about two thousand years old in his current form. As the Maia Olórin he existed before Middle-Earth was created.
Every last named elf is this as well, with Círdan being the oldest of all elves that haven't set sail to Valinor. (It's probably relevant that Círdan is the only Elf in the entire story who's explicitly stated to have grown a beard, let alone a long white beard.)
Reasonable Authority Figure: It takes Gandalf some ingenuity to restore Théoden's past judgement, but after Gandalf succeeds the King of Rohan is one of the main assets to the Free Peoples. Gandalf tries later to talk sense into Denethor, this time to no avail.
Recurring Dreams: Faramir, twice. One of these is based on the 'great wave' dream that both Tolkien and his son Michael had.
Red Eyes, Take Warning: Sauron's symbol is a red eye on black, and the Mûmak (giant elephant) in The Two Towers has raging small red eyes.
Red Pill, Blue Pill: Frodo is given the choice to unburden himself of the Ring and its mission several times throughout the story, but he never chooses to return to normalcy.
Redemption Equals Death: Boromir dies trying to defend Merry and Pippin from capture, after his attempt to seize the Ring sends Frodo fleeing and the rest of the Fellowship runs hither and yon trying to find him.
Reforged Blade: Narsil, sword of Elendil, which was shattered - but the hilt-shard cut The One Ring from the finger of Sauron, thus winning the war. Much later, they were reforged for Aragorn's use and renamed Andúril. He never does anything 'special' with the sword, but since it serves as a symbol of his status as the Returned King, and since the reforging was part of a series of prophesied events leading up to the final fall of Sauron, it qualifies as a Sword of Plot Advancement.
Refused by the Call: A 128-year-old Bilbo Baggins is the first to offer himself as Ringbearer for the Quest of Mount Doom, but is gently refused by Gandalf and Elrond as too old and too vulnerable to the Ring.
Regent for Life: Denethor. Though he actually has a good precedent for not accepting Aragorn's claim — especially since he has reason to believe Aragorn won't act in Gondor's best interest — and we don't know what he would have actually done had he not been Driven to Suicide. So it's certainly not a clear-cut example.
Rejection Ritual: Gandalf the White casting Saruman out of the order of wizards, culminating in the breaking of Saruman's staff.
Reluctant Gift: The One Ring has this effect on its bearers, to the point that few will give it up willingly. Most notably, Bilbo Baggins has to be prompted into giving it up when Gandalf tells him, "The Ring is still in your pocket."
The Remnant: Saruman qualifies in a round-about sense, in that he is a former "Evil Overlord", but reduced to a pathetically small scale after his armies are routed and he is cast out from Isengard. He spends the remainder of the book running the Shire into the ground, turning into a sort of bandit leader with a mob of "ruffians". He gets his throat cut by his much-abused servant at the end.
Repeat After Me: A very rare dramatic usage. After being visited by Sauron through the palantír, Pippin in his terror repeats — as well as he can — the exact words of Sauron's intended message for Saruman:
Sauron, to Pippin: Tell Saruman that this dainty is not for him. I will send for it at once. Do you understand? Say just that!
Pippin, to Gandalf: It is not for you, Saruman! I will send for it at once. Do you understand? Say just that!
Rhyming with Itself: One of the parts of Sam's Oliphaunt poem rhymes "Me" with itself, but it's worth noting the poem is more whimsical than most others throughout the story. Also, in this case it's only half of a two-syllable rhyme:
If ever you'd met me / You wouldn't forget me.
Riddle for the Ages: Early on Sam passes along a second-hand report about an Ent-like creature roaming the northern fringes of the Shire, but no further information is ever forthcoming.
Passing over (Caradhras)/under (Moria) the Misty Mountains was this trope for the Fellowship.
Frodo and Sam have to get into Mordor. How? By climbing up hundreds of "stairs" on an almost vertical mountain and crawling through a giant spider's lair. Because they obviously can't use the front gate.
Aragorn has to go through the ghost-infested mountains that no-one has ever returned from before. Though perhaps in this case the trope is not entirely played straight since he went in there to gain the alliance of said ghosts...
The Rohirrim avenging Théoden's death on the Pelennor Fields.
Rousing Speech: Given by Aragorn at the Stone of Erech and Théoden before the Battle of the Pelennor Fields, then subverted by Éomer during the same battle; after he finds his sister Éowyn, apparently dead, he just shouts, "Death, death, death! Death take us all!" and leads the Rohirrim in a reckless charge. When the charge falters, then he gives a speech... about how hope is lost and they're going to go down fighting. note Both parts were given to Théoden in the movies, some at Helm's Deep and some in his "Let's All Go And Get Killed" speech.
Royal Blood: Flows in Aragorn's veins and is rather important.
Aragorn again, as well as Théoden, Théodred, Éomer and Éowyn. Legolas and Imrahil are princes, and Boromir and Faramir are sons of the Ruling Steward, Denethor (whose ancestors were hereditary stewards even when there was still a king in Gondor). Merry and Pippin are eldest sons of the rulers of Buckland and the Shire, respectively.
The same goes for Brand (King of Dale) and Dáin II Ironfoot (King Under the Mountain), whose deeds are mentioned only in the appendices.