Nazgûl AppearNazgûl Appear - Of the Rings which were forged, only the Nine that were gifted to the race of Men had the effect Sauron intended.  As mentioned, the Three Elven Rings were beyond his control (see Narya, Nenya & Vilya), and the Dwarves prized theirs only for their value, and did not wear them.


"The Dwarves indeed proved tough and hard to tame, they ill endure the domination of others, and the thoughts of their hearts are hard to fathom, nor can they be turned to shadows.  They used their rings only for the getting of wealth." ~The Silmarillion (Of the Rings of Power and the Third Age)


The hearts of Men, however, are easier to corrupt, and the nine who were given Rings, over time, were bent to Sauron's will.


"Men proved easier to ensnare.  Those who used the Nine Rings became mighty in their day, kings, sorcerers, and warriors of old.  They obtained glory and great wealth, yet it turned to their undoing.  They had, as it seemed, unending life, yet life became unendurable to them.  They could walk, if they would, unseen by all eyes in this world beneath the sun, and they could see things in worlds invisible to mortal men, but too often they beheld only the phantoms and delusions of Sauron.  And one by one, sooner or later, according to their native strength and to the good or evil of their wills in beginning, they fell under the thraldom of the ring that they bore and under the domination of the One, which was Sauron's.  And they became forever invisible save to him that wore the Ruling Ring, and they entered into the realm of shadows.  The Nazgûl they were, the Ring-wraiths, the Enemy's most terrible servants; darkness went with them, and they cried with the voices of death." ~The Silmarillion (Of the Rings of Power and the Third Age)


Not even the Men of Númenor were immune to the Rings' effect.


"But Sauron is ever guileful, and it is said among those whom he ensnared with the Nine Rings, three were great lords of Númenórean race." ~The Silmarillion (Akallabêth)