Tolkien was the single biggest influence on D&D. The fantasy supplement for Chainmail was based on
a Lord of the Rings wargame created by Leonard Patt. Chainmail is full of Tolkien references such as "hobbits", "nazgul", "ents", "balrogs", "werebears", and even "Orcs of Mordor" and "Isengarders" (another type of orc). Tolkien is one of three named authors, the others being RE Howard and Poul Anderson, and the only one to be mentioned three times.
All of these made it into OD&D, and most had to be renamed after a 'cease and desist' letter in 1977.
D&D still contains the following elements derived from Tolkien:
PC races – elf, dwarf, halfling, half-orc, half-elf
Class – ranger
Monsters – orc, goblin, warg, wight, giant eagle, werebear, treant, type VI demon, red dragon
Spells – fireball, lightning bolt, light, hold portal, knock, produce flame, ventriloquism
Magic items – mithril, elven cloak, ring of invisibility
In terms of broader themes, the D&D adventuring party is Tolkien-esque, as is the 'racial geography' of D&D worlds - elves in the forests, dwarves/orcs/goblins in the mountains and underground.