Most modern D&D players take it as an undeniable truth that Dungeons and Dragons is a blatant ripoff of The Lord of the Rings, and just the Lord of the Rings. They will deny that the game takes any significant inspiration from the works of authors such as Vance, Leiber, Moorcock, Howard, Burroughs, Anderson, etc. and certainly not that each of those authors was a greater influence on the game than Tolkien was. This is especially bizarre with Vance, as the term "Vancian Magic" still gets used to describe the classic D&D magic system, and yet the idea that D&D might be pulling more core concepts from Vance's Dying Earth books is treated as absurd. In this essay we'll explore why the thought of D&D as a LOTR ripoff is absurd, why so many gamers believe it anyway, and why it is especially absurd for them to believe this even in their ignorance, considering how they play the game.
First let's get this out of the way: I'm not claiming that there is no influence of JRR Tolkien's works on on Dungeons and Dragons. It does appear on Appendix N, Gygax refers to the Hobbit when discussing the transportation of treasure, hobbits and balrogs were taken wholesale, etc. I want to begin by acknowledging this because many of the people who insist that D&D is just a LOTR ripoff assume that anyone saying otherwise denies any influence. "But the Tolkien estate took legal action against them, case closed!" It's dumb, but people do it, so we need to get that out of the way.
What that argument of course ignores is that there are many things in Dungeons and Dragons which were shamelessly taken from other sources. The depiction of paladins and trolls is directly out of Poul Anderson's Three Hearts and Three Lions. The alignment system of original Dungeons and Dragons closely resembles the alignment given in that story, though later developments are more akin to Moorcock's stories (with maybe a touch of the conflict in Zelazny's Amber series.) Magical swords might as well be named Stormbringer. The depiction of wererats and thieves guilds is from Fritz Leiber. They tried to use the Elder Gods from the works of Lovecraft and related authors, until they faced legal action from Chaosium (which by the reasoning of supporters of the Tolkien theory, should prove that D&D is a Cthulhu Mythos ripoff.)
But the most blatant influence is that of Jack Vance. The magic system is still known as "Vancian Magic" because it is taken directly from Vance's Dying Earth stories. This is pretty obvious both in terms of effect and flavor. But we don't even need to extrapolate on this one; in the 1st Edition AD&D Dungeon Master's Guide Gygax explicitly advises DMs to direct players to Vance's The Dying Earth and The Eyes of the Overworld to understand how spellcasting works (as well as John Bellairs's The Face in the Frost, though Gygax has said that he read that one too late for it to form the genesis of the spellcasting system, it just nicely complements the ideas.) Ioun stones (or IOUN stones as they appear in Vance's work) are directly taken from the Dying Earth stories. More than this, the general feel of the D∧D universe far more closely resembles The Dying Earth than the Lord of the Rings. In Tolkien's works, there are only five wizards who are not human and only one of them seems to have a base of operations. In D&D and Vance's works, humans can learn to become wizards (though the task plays havoc with the human brain, hence why spells need to be remomorized) and it is very possible to encounter a random wizard in a tower who is conducting a variety of experiments on magical items and creatures. The idea of the D&D thief is nicely summed up in the character of Cugel from The Eyes of the Overworld, right down to the ability to read spells from scrolls (though this may also have been influenced by the fact that the Fritz Leiber's Gray Mouser was an apprentice wizard before he became a scoundrel and adventurer.) The ruins of lost civilizations are common, and those who encounter them are more concerned with how best to exploit the spoils than they are with wondering at them.
Of course, this is not to say that Vance's works are the only influence on D&D. We've already listed others. But they are probably the greatest influence on the setting, and certainly far more of an influence than the Lord of the Rings was.
The funny thing is, people who claim that the Lord of the Rings was the biggest influence actually ignore several parts of the game which can follow the works of Tolkien, since they are almost always bound to "conventional play." That is, a campaign following a single party that does not engage in domain level play or mass combat, and where time is treated haphazardly. Yet in the Lord of the Rings the party splits repeatedly, being in four different parts at one point in The Return of the King (Frodo and Sam in Mordor, Pippin and Gandalf in Minas Tirith, Aragorn, Legolas and Gimli with the armies of the dead, and Merry with the armies of Rohan.) It's worth referring to Shamus Young's DM of the Rings here, which reinterprets the Lord of the Rings as a D&D session. Note that in this narrative the breaking of the Fellowship is interpreted as most of the players leaving for another RPG session, with only the Aragorn/Legolas/Gimli group remaining as an actual party. The idea that the party could split is seen as so impossible that Shamus doesn't pursue it (though to be fair to him, he might have wanted to show the inevitable drama induced break-up as the comic is more about D&D than the Lord of the Rings.)
Similarly, the large battles are one of the most famous aspects of the Lord of the Rings. How many Battle of Helm's Deep maps were there for Warcraft III? And wargamers have been playing that battle, as well as Minas Tirith, ever since the books were written. Yet in conventional play such battles are impossible. At best players will hear about a battle going on in the background, or maybe personally kill 20 orcs in a battle between tens of thousands of participants, without being able to contribute to the overall strategy. Aragron is a king and rules over his kingdom, but no domain level play in modern D&D. Throughout the story the march of the armies of Sauron and his allies are stressed, so that if the One Ring is not destroyed quickly enough all will be lost. But conventional parties move at the speed of plot, and they have to because no one bothers tracking how long anything takes and they certainly don't have antagonists moving on their own while the party dicks around wasting time.
Outline for later: compare things like wizards in LOTR versus Dying Earth to establish the non-Middle Earth nature of the setting. For part two, refer to the literary ignorance of modern players. Be sure to handle the "but they were sued by Tolkien's estate!" claim that is being made, since that of course only implies that some small aspects of the game came from Tolkien, not that EVERYTHING can from Tolkien. For the third part, note that modern gamers hate things like splitting the party, long travel narratives, mass combat, etc. despite these being huge parts of both the Lord of the Rings and the Hobbit.