The One Ring is power. This seems largely without opposition in Tolkien’s opus: they who wield the ring have the might to dominate the peoples of Middle-Earth. What does it mean, though, to dominate? To desire the ability to impress one’s will upon the freedom of sentient beings? It means to subvert the good works of God, to attempt to pervert them to something apart from Creation. That, is evil. Sauron created the One Ring with his malice in the desire to rule the minds of the world. Desire to rule, desire for power over creation—a wish to extend oneself into and over the world and to be adored for it. In a single phrase, this evil is a self-worship.
Sauron is definitely one of the more blatant of cases, though self-worship as evil arises in a number of spots in the Lord of the Rings. Those men who were ensnared by the One with the Nine gained power and wealth over their people ; Fëanor gloried in his radiant gems, reveling in the praise of his creation and loathe to part with them ; in brief possession of the Ring, Sam saw himself a powerful warrior in possession of a garden of the lands; the Númenórian kings fancied themselves, in their adoration of self, equals to the Valar, and others. Those who succumb to the desire of self-worship are those doomed to evil.
So how then do we describe evil’s ever-present foil, those who are good? Simply taking that distillate of evil (self-worship), its opposite stands as self-denial. That is, denial of the extraneous desires of the individual in the light of preserving the freedoms and wills of others. Sam is able to give up his desires for glory by focusing on his master. Gandalf passes his test through his desire to preserve the freedoms of Middle-Earth. Frodo willingly sacrifices himself through his journey and humility, fully expecting to not survive the venture for, at first, the good of the Shire, and later Creation.
In light of this opposition, the allure of the Ring—and that power to dominate that it represents—is curious. The Ring is possessed of a will of its own, influencing and seeking the one through which it can dominate. Its influence is, as Shippey notes, addicting, and the desire to impose one’s will grows steadily in the minds of those around or in contact with It, corrupting them with aspirations of absolute power.  Why is it that “power corrupts, and absolute power corrupts absolutely?” Are all sentient beings possessed on some level of the desire of self-worship? For it seems that this dedication to power is ultimately undoing: Gollum’s addiction to the power of the Ring and his struggle with Frodo leads ultimately to the Ring’s demise; Melkor and Sauron, in their respective quests to dominate, were ultimately undone more completely than they sought to impose their wills. The worldly content of good and evil tends to flow in cycles, that evil might arise anew and ultimately be destroyed—that, in another cliché, the “good guys always win in the end.”
What is it that causes this case of good-versus-evil to arise in cycles? If the addiction and draw to evil ultimately destroys those who indulge the wiles of the Ring, why should the world not be all-good? The bare beginnings of the answer may lie in the fact that good and evil are a self-consistent dialectic—should one (e.g. good) exist, then so too must the other by way of absence or denial (e.g. evil). In this framework, there is always the potential for evil to arise where there is good—in Biblical terms, following the Original Sin.
It may be that, as mortal beings—or even immortal—apart from and incapable of perceiving the Mind of God, that we shall never know the reason for these cycles. Tolkien certainly offers no explanation—Melkor, in his apparent free will, always sought and desired the Imperishable Flame.  Sauron is tempted and falls with the will of Melkor. Countless others, in their free will, turn to the power and impressing will of the Enemy. It is possible that the potential for evil—for the desire of self-worship—is simply a facet of free will itself. If it were not, then it would not be “free” will; though why this may be is known fully only to God.
 “Man is a wolf to man,” Roman proverb; referenced here that man preys upon himself and others
 Mark 12:31.
 Tolkien. Silmarillion 289; kings of men glorify themselves by the stature of their position and wealth
 ibid. 78; this small example, while not perhaps on the level of Sauron or the Nazgûl, does epitomize the (start of the) fall from grace that is visible in the fall of the Númenórians
 ibid. 301. Shippey. The Road to Middle Earth 139
 Silmarillion 16.