Well, we all know that D&D is roughly based on LotR, changed just enough so that they don't have to pay royalties/get sued
From there, it's evolved.
It doesn't really take much effort though to make a Tolkien D&D world. Let's face it... there really isn't that much to it in all but one aspect. You've got humans. More humans. A bunch of halflings. Some elves. Some half-elves. Dorfs. And some big eagles. And against that you have humans. Orcs/goblins. Wargs. And what basically amounts to 9 liches. Throw in a few 'trolls' (basically ogres that can't stand daylight), a werebear, and some ents. So for critters, it's all pretty easy.
Modify races a bit... or make kits. So dwarves get bonuses with battle axes and elves with bows. Give the horse guys some special horse related skills, like +1 to hit when mounted or something. All cake. The world, the cities, the people, all described.
What is hard though is getting a feel for the magic. Magic is either common or very hard, depending upon what Tolkien needs at the moment. Basically, magic done in a lab or to make harmless expendables (like fireworks) is pretty easy. Magic to make enduring items is hard, but done from time to time. Magic out in the field in combat is hard. You'll notice very few spells are actually cast in LotR. D&D, however, is set up to make spells common. There are no clerics, pretty much. So you can get rid of them. But that leaves you with the wizard. What do you do with spell casters? Effectively, you can get rid of them as well. For in such a magically sparse world, any magician type character would rapidly grow bored. If you alter the magic, introduce clerics and what-not, you've dramatically changed the feel of the world.
And so there your characters are, wandering through a magically sparse world where they can't be the main movers and shakers, where whatever enemy they face pales in comparision to the true evil. Even if you involve them in the fight against Mordor, they can't be the ones to destroy the main evil. At best they can be something that distracts him and therefore lets the Ringbearer do his duty. All without healers or magicians. And in a world where every player has his views of it all... and woe be to any GM that alters things.
Why would you want to play in such a time and world? To do it as a tribute... a similiar plot in a different world, such as Shadow Run or whatever... a place where the rules are different and so the players can be the main characters, can alter things, can be classes that don't fit the world... and you can throw the unexpected at them.
Maybe it's just me... but I'd rather play in a world where, if I'm the GM, I'm free to do what I want. And where if I'm the player, I've got no qualms about what the GM is doing... and while events are happening around me, what I do can make a big difference.
>>Would that famous harper fare as well against Balrog?
Well, how much effort does it take to fall off a bridge, fall for a very long time, wet oneself (which properly treated can bleach), wind up with white robes, and land on top of a fluffy balrog. Then go out and talk big to your friends (who are too dumb to realize the limits of your magic are fireworks, smoke rings, and burning pine-cones... assuming he didn't have a lighter) about how you fought long and hard