If Sauron had never made thye one ring, there would never have been the Last Alliance since he would have been killed in the drowning of Numenor. He was only able to survive that because the ring 'anchored' him to middle earth, allowing him to return. Also, if Sauron had never made the one ring, it is possible that he never would've been tangled up with the Numenoreans as he couldn't have defeated the elves and taken over ME without his ring.
So if Sauron never made the ring it is conceivable that Ar-Pharazon would never have attacked Valinor, leading to the drowning of Numenor and the removal of the uttermost west from the circles of the world.
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His sword was long his lance was keen
His shining helm afar was seen
The countless stars of heavens field
Were mirrored in his silver shield
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