As the others have said Sauron had poured his power into the Ring, and if the Ring was destroyed (or mastered by someone else) Sauron's 'bond' to the Ring would be broken:
Quote:
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But to achieve this he had been obliged to let a great part of his own inherent power 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 siutation in his effort (largely unsuccessful) to enslave the Elves, and in his desire to control the minds and wills of his servants. There was another weakness: if the One Ring was actually unmade, annhiliated, then its power would be dissolved, and he would be reduced to a shadow, a mere memory of malicious will.~Letter to Milton Waldman
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The Ring's power (which was Sauron's) were bound, or in 'rapport,' if that bond was broken Sauron would be killed. His spirit wouldn't be destroyed, because that seems to be something impossible to do. But, as the other posters have said, he would never again be able to take a physical form.