The main races of Middle Earth are Elves, Men, Hobbits and Dwarfs. For the purposes of this discussion, we choose not to list the Orcs as distinct from the Elves because Orcs and Elves came from the same original creation, whereas Men and Dwarfs were created separately. As for Hobbits, their origin is a mystery. We will also use the term 'humans' interchangeably with 'Men'.
In the Chapter "The Beginning of Days" in the Silmarillion, the will of Iluvatar, the supreme Creator, concerning His Children (Elves and Men) is revealed (Quendi refers to the Elves and Atani refers to the humans):
"...the Quendi (Elves) shall be the fairest of all earthly creatures, and they shall have and shall conceive and bring forth more beauty than all my Children; and they shall have the greater bliss in this world. But to the Atani I will give a new gift."
Elven superiority seems divinely ordained, but perhaps a case can still be made for the "different but equal" status of humans. For the gift that humans have is to "have a virtue to shape their life, amid the powers and chances of the world, beyond the Music of the Ainur, which is as fate to all things else."1
In other words, humans, unlike Elves, have the power to shape their own destinies, beyond the designs of the created gods, and will go to a fate beyond the physical world. But Elven superiority to humans remains a constant theme in LOTR and its companion works:
"In those days Elves and Men were of like stature, and strength of body, but the Elves had greater wisdom, and skill, and beauty; and those who had dwelt in Valinor and looked upon the Powers as much surpassed the Dark Elves in these things as they in turn surpassed the people of mortal race. Only in the realm of Doriath, whose queen Melian was of the kindred of the Valar, did the Sindar come near to match the Calaquendi of the Blessed Realm."2
It is also implied that the Elves, unlike humans, were all of the white race. As described in Unfinished Tales, the Easterlings, a human race, named the Elves "white-fiends".3 The implication is, of course, that the Easterlings aren't white-skinned, which Tolkien confirms in the Silmarillion. (See the article Human Races in Middle Earth.)
In the chapter Of the Coming of the Elves in The Silmarillion, it is told that the god Orome came among the Elves, and "all the noblest of the Elves" were drawn towards him. But other Elves, presumably less "noble", were afraid of Orome, so they "fled and were lost".
The Orcs or goblins were descended from these less "noble" Elves who were captured by Melkor/Morgoth, the Devil. Melkor bred "the hideous race of the Orcs in envy and mockery of the Elves" by corrupting and enslaving his Elven captives. They are the evil race in the LOTR universe.
In The Silmarillion, dwarves were implied to be an inferior creation to both Elves and humans because unlike Elves and Men, they were created by Aule, a created god, and not by Iluvatar, the supreme Creator. Yet Tolkien also implies their superiority in some aspects - they were stronger than humans and lived longer. Dwarfs in general also had superior mental strength compared to Elves and humans. Many among Elves and Men had been mentally enslaved by Morgoth the Devil, but Dwarfs were more effective at resisting him, due to their famous Dwarven stubborness. They were described as more skilled in craft than even the Noldor, most skilled among Elves.
The dwarf characters in the Silmarillion were mainly evil, but as a group, they did join Elves and "good" humans in the battle against the devil. In the Hobbit + Lord of the Rings quadrilogy, dwarves were at least on the "good" side. Tolkien's treatment of dwarves is more positive and varied than his treatment of non-white humans, such as the Easterlings and the Haradrim, who were consistently portrayed negatively.
Hobbits were said to be "akin" to humans, but this similarity is cultural - they like the same things that humans like. Tolkien says nothing about their creation. Hobbits are pointy-eared, unlike humans. They live longer than humans but not as long as dwarves. Like Elves and humans, Hobbits are also subdivided into different strains. Other articles will explore these internal divisions within the main races.
LOTR, The Silmarillion and Unfinished Tales, taken together, send mixed messages about the biological basis for racial superiority. On one hand, Tolkien is very clear that certain peoples become superior to others - "fairer" and "wiser" and "stronger" because of their environment (in the case of the Elves of the Light vs. The Grey Elves vs the rest of the Dark Elves) or their works and choices (as in the case of the humans). But on the other hand, distinguishing physical traits are sometimes associated with certain races which are considered higher, or lower. (As in the case of the Vanyar vs the Noldor, and the Edain vs the cruel Easterlings and the Haradrim).