[The Squatter of Amon Rûdh]

But to achieve this he had been obliged to let a great part of his own inherent power (a frequent and very significant motive in myth and fairy-story) pass into the One Ring. While he wore it, his power on earth was actually enhanced. But even if he did not wear it, that power existed and was in 'rapport' with himself: he was not 'diminished'. Unless some other seized it and became possessed of it. If that happened, the new possessor could (if sufficiently strong and heroic by nature) challenge Sauron , become master of all that he had learned or done since the making of the One Ring, and so overthrow him and usurp his place. This was the essential weakness he had introduced into his situation in his effort (largely unsuccessful) to enslave the Elves, and in his desire to establish a control over the minds and wills of his servants. There was another weakness: if the One Ring was actually unmade, annihilated, then its power would be dissolved , Sauron's own being would be diminished to a vanishing point, and he would be reduced to a shadow, a mere memory of malicious will. But that he never contemplated nor feared. The Ring was unbreakable to any smithcraft less than his own. It was indissoluble in any fire, save the undying subterranean fire where it was made - and that was unapproachable, in Mordor. Also, so great was the Ring's power of lust, that anyone who used it became mastered by it; it was beyond the strength of any will (even his own) to injure it, cast it away or neglect it. So he thought.

From letter #131 to Milton Waldman

Essentially, then, Sauron's power, once built into the Ring, was separate from his person and therefore able to be usurped or dispersed by others; but only by those sufficiently strong-willed to command it rather than becoming its slave as did Gollum. It is unlikely that Galadriel had the strength to do this (I expect that her apparent belief that she could was either a delusion of the Ring or an attempt to demonstrate to Frodo the dangers of giving it to one of the Wise), but Gandalf might have done, and Saruman certainly thought that he could bend it to his will. Unfortunately the Ring corrupts of and by itself: any works attempted with it would inevitably turn to evil, which is why both Gandalf and Galadriel ultimately reject it. Tom Bombadil is unaffected, according to another of Tolkien's letters, because he has no interest in what it represents:

...but both sides in some degree, conservative or destructive, want a measure of control. but if you have, as it were taken 'a vow of poverty', renounced control, and take your delight in things for themselves without reference to yourself, watching, observing, and to some extent knowing, then the question of the rights and wrongs of power and control might become utterly meaningless to you, and the means of power quite valueless.

In other words, true victory over Sauron, such as that in The Lord of the Rings can only be achieved by the utter rejection of his tools and methods, as exemplified by the One Ring. Rather a neat device in my opinion, and very much from the heart.