Nazgûl
The Nazgûl, also called the Ringwraiths, the Nine Riders, or the Black Riders, were the most terrible of Sauron's servants in Middle-earth -- nine Men of old who had fallen utterly under his dominion through the power of the Rings of Power. In the Second Age, Sauron gave nine Rings to mortal Men, kings and sorcerers and warriors. One by one their bearers were ensnared, their lives unnaturally prolonged until existence became an unending weariness, and at last they faded out of the seen world altogether, becoming wraiths enslaved wholly to the will of the One Ring and its master.
Invisible under their black robes and hoods, the Nazgûl could be perceived in the unseen world or by their dreadful presence. Their chief weapon was terror: the Black Breath that they spread brought despair, sickness, and death, and few could stand against the fear that came with them.
The Lord of the Nazgûl
Greatest among them was the Witch-king, the Lord of the Nazgûl, who in an earlier age had founded the dread realm of Angmar in the north and warred long against the kingdoms of the Dúnedain. A prophecy held that he would not fall by the hand of any man -- a doom that came due upon the field of the Pelennor.
History
The Nazgûl rode out from Mordor in the guise of Black Riders to hunt for the One Ring when Sauron learned it had been found, pursuing the hobbit Frodo from the Shire to the very Ford of Bruinen, where they were swept away by the flood of Rivendell. Later they took to the air upon hideous winged beasts, becoming swift terrors over the battlefields of the War of the Ring. At the Battle of the Pelennor Fields the Witch-king slew King Théoden of Rohan, only to be destroyed by Éowyn -- no man, but a woman -- with the aid of the hobbit Merry.
Significance
The Nazgûl are the very embodiment of the corrupting power of the Rings: mortal men granted false immortality, hollowed out and enslaved until nothing of themselves remained but Sauron's will. They are bound utterly to the One Ring, and at its destruction in the fires of Mount Doom they perished with it, undone in the same instant as their master.