Gary Gygax downplayed Tolkien's influence a lot later, but it's quite obvious from the races & classes available that Tolkien
was a major influence.
However, the style of adventure and the mechanics of early D&D weren't all that influenced by Tolkien. Instead you have Jack Vance, Fritz Leiber, Edgar Rice Burroughs, R.E Howard and other authors who really influenced the early game.
See here:
Appendix N - Gary's D&D Book Inspiration List
Cheers!
This won't be popular...but I blame Arneson for that. Arneson was much of the brilliance behind the original, inclusive of HIS default combat system which eventually became the Default combat system for D&D...But NOT before it was the optional system with Chainmail as the primary.
Arneson's influences came from everywhere and everything. If someone had a good idea, well...why not simply toss it into play. So you get this Vancian magic with some Sci-Fi elements, and Naval combat systems with medieval warriors.
Gygax was the economic and purpose driven genius who got things done. If Arneson was the soul, Gygax was the brains. Chainmail came into the picture because Gygax wanted it in the picture...the optional system (AC vs a roll) took over because players decided differently. I actually think Gygax was heavily influence by Tolkien as was everyone else.
However, a lot of the other players read a LOT of fiction and had zany ideas of their own...inclusive of other writers. Of course everyone else would read those writers eventually, and so I suppose could claim that influence, but in truth...that original source of why it came in could be pinpointed to a particular person probably. Some of them may not have even realized they were the original source...as it probably came up that they asked if they could do something or whatever...and maybe said where the idea came from...and there you go.
So, it became a mish mash...but Arneson's stuff was always more humorous in ways and campy then Gygax's. Far more outlandish and evolving based on what players brought in.
Just take a look at what became of Blackmoor and all it's elements in relation to GreyHawk.
I think there were more Grey Hawk fans in the long run though.
Just my opinion...and a very minor opinion amongst everyone here I suppose...but just my two coins on what was happening during the origins of it all.
Then again, I think the main complaint that could be levelled against me was that I was always more of the wargamer than the RPG player...and dealt more with the Wargaming sides of the coin than the RPG's...so what would I know anyways!