As I've been going through the minutiae of the AD&D game as I am working on the manuscript for Adventures Dark and Deep™, however, I am noticing quite a few more subtle (and not-so-subtle) influences from Professor Tolkein's works on the game. I am becoming ever-more convinced that Gygax's attitude was influenced by the lawsuit from the estate of Prof. Tolkein that famously forced TSR to change hobbits to halflings and ents to treants, and may well have been an effort to avoid another. However, the concept of half-elves seems derived from Elrond.
The whole idea of the ranger class, for example, is taken whole cloth from Aragorn and the other rangers. Details such as their propensity to operate alone or in small groups, as well as their abilities with tracking (as we see when Aragorn is trying to figure out what happened to Merry and Pippin), make this plain.And at 10th level they gain the ability to use scrying devices... like crystal balls (palantirs). Seems a random ability, if not for the Tolkein connection.
However, we also have the cloak of elvenkind; an obvious nod to the cloaks that the Fellowship are given by the elves. Too, we have the crystal hypnosis ball, that gradually brings the user under the thrall of some off-stage evil force; clearly a reference to the palantirs as used by Saruman and Denethor. The retributive strike of both the staff of the magi and the staff of power seems inspired by Gandalf's battle with the Balrog. (Speaking of which, the Type VI Demon is clearly more than inspired by that most lethal of the denizens of Moria, right down to the flaming whip.) The ability of giants to hurl boulders is not, to my knowledge, found in any source prior to The Hobbit, where the thunder of the storm that forces Bilbo and company to seek shelter in the cave in the Misty Mountains is compared to the sound of the giants in the mountains hurling boulders to amuse one another.
The drums of panic may well be a reference to the drums sounded by the orcs of Moria... "the drums in the deeps." Could the ring of elemental command have been inspired by the rings of the elvish kings, which were attuned each to a different element? (Agreed, 3 in Tolkein and 4 in Gygax, following the classical Greek assignation of the elements.) It's certainly possible. The rope of climbing bears an uncanny resemblance to the elvish rope that Frodo and Sam use to penetrate the outer barriers of Mordor. I am sure there are many other examples that could be cited.
I don't say that (A)D&D was entirely inspired by Tolkein, but I am pretty sure that the influence of Tolkein on the design of the game was much greater than Gygax let on.