Sauron was one of the Maiar, from the dawn of creation. At some point he had a mortal body, lost in the fall of Númenor. He later guided the creation of the Rings, then made the One Ring personally. He lost the Ring, then tried to regain it. How does his power level vary across this timeline? How does it compare to other beings?
Sauron himself was quite powerful, being a Maiar and indeed the chief Maiar of Melkor in his rebellion. This would have put him in a similar position to that of Eonwe, the Maiar who lead the war against Morgoth who was described in the Silmarillion as
greatest of arms in Arda
Even before the rebellion Sauron was being described as
a great craftsman of the household of Aulë (HoME)
In his beginning he was of the Maiar of Aulë, and he remained mighty in the lore of that people. (Silmarillion).
We can skip over the War of Wrath since you asked specifically about the Ring. However, as an unbound Maiar, his powers were already more significant than most others in Middle Earth as there were no others remaining in Middle Earth of his stature... up until the Elven Rings were being made:
for the power of the Elven-Rings was very great, and that which should govern them must be a thing of surpassing potency. (Silmarillion)
a great part of his own former power (LotR)
into the Ring, and used it to enhance Sauron's own power (think of a man creating a telescope to "enhance" his power of sight). Thus the Ring made him even more powerful than was previously the case, sufficiently powerful to not worry about the Elven Ring bearers as was his intention.
According to Tolkien Sauron wasn't actually reduced in power while not in possession of the Ring (Letter 131):
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’.
So he wasn't significantly diminished from his original power, as long as the Ring existed. It was only the destruction of the Ring or the claiming of it by others that would have caused him to lose that power.
- Sauron with his original powers was more powerful than anyone bar an Elven bearer of an Elven Ring (Wizards were not around prior to the Rings being forged, so can't be read into the Silmarillion's comment);
- Sauron with his Ring was the most powerful being in Middle Earth;
- Sauron without his Ring was still a very powerful being in Middle Earth - some or all of the White Council, which included the Elvish Ring bearers Elrond and Galadriel, a Wizard with a Ring in Gandalf, plus Saruman, Radagast and Cirdan, were needed to overthrow his servants directly in Dol Guldur with an expectation to face Sauron himself;
- Sauron with the Ring claimed by someone else or if it was destroyed would just be "a mere shadow".
By the way, Sauron did have the Ring in Numenor:
He naturally had the One Ring, and so very soon dominated the minds and wills of most of the Númenóreans. ... Though reduced to 'a spirit of hatred borne on a dark wind', I do not think one need boggle at this spirit carrying off the One Ring, upon which his power of dominating minds now largely depended. (Letter 211)
Sauron started as sort of a mid level Maiar, before becoming the main servant of the Vala Melkor (aka Morgoth) after Melkor's rebellion (there are some parallels to Lucifer in Christian theology). The Valar were like the Maiar but more powerful. So Sauron became fairly powerful by association. Although he never permanently inhabited a mortal body, Sauron could, like all Maiar, take a mortal form if he desired.
After the fall of Numenor Sauron was punished in that he could never again take pleasing form, diminishing his ability to decieve others - a significant reduction of his influence, if not of his innate magical power.
Sauron's creation of the One Ring allowed him to control those who used the lesser Rings (except the Elves), which returned some of the influence he lost after the fall of Numenor. However, something like 90% of his power was bound up in the ring, so when he lost it he was reduced to almost nothing.
By the time of the events of LotR, Sauron had regained much of his influence, if not neccessarily his innate power (still bound in the lost Ring). He had the largest armies in Middle Earth; had he regained the ring he would have been the single most powerful being in Middle Earth even without the armies.
That's the best summary I can give, based on my recollection of the Silmarillion and LotR; if anyone can improve or expand, please do.
Sauron had the power to shape-shift into various, beautiful forms, as well as turning into a werewolf, all of this in the Silmarillion. He also made the rings when Numenor was still in its golden age, and waged war against the free peoples of Middle Earth until Ar-Pharazon decided to amass a vast host and storm his lands, because Sauron had called himself the "King of Men", and the Numenorians didn't agree to this idea.
Contrary to what others have written, Sauron was described as being the most powerful Maiar of them all, second only to the Vala, and he was originally called Mairon, in the service of Aule, who was the Valar patron of craftsmanship, forging, and all things to do with the earth itself. It is through his time of service to Aule that Melkor caused Sauron to admire him, for Sauron loved order, and Melkor often appeared to desire an ordered world. It is also through this time of service to Aule that Sauron learned a great deal about all of Aule's craft, as well as understanding many things concerning the earth, craftsmanship of many kinds, and industry itself. With this knowledge, not only was he able to direct the smiths of Eregion into forging the great rings and himself forging the one ring, but that he was also able to teach languages to the orcs, teach trolls the black speech, build vast fortresses like the black gate and Barad-Dur, and amass vast hosts of orcs as well as armies of evil men, all the while providing for their armor and food and upkeep.
Physically, he was extremely powerful. Even if the Wizards were not limited in their powers, Sauron was stronger than any one of them, and with the ring, stronger than all of them. Even the Elves with the Elven rings could only do so much against Sauron, as they immediately took off the rings when they sensed Sauron's presence through the one ring. They were able to use the Elven rings in the time where Sauron was without the ring solely because he wasn't wearing it at the time. The rings themselves were meant to empower their wearers with a host of abilities and passive benefits, but the one ring itself was designed to lord over all the other rings, allowing Sauron to control the minds and thoughts, as well as seeing the thoughts, of the wearers, for it was his desire to dominate the minds of his enemies and turn them into his mental slaves, as he greatly desired the Elves to be in his service.
After the fall of Numenor, he actually lost much of his power, due to his body being destroyed, and forever after he was stuck with the appearance of a terrible dark lord, and he could no longer take on the beautiful forms which he was so infamous for. Yet because he had the ring, and because he poured so much of his power into it, that even though he lost his body, rather than being reduced to a mere shadow, he was still powerful and mighty and a force to be feared. In the Second and Third Ages, with the enhanced powers that the ring gave him, he was the single most powerful being in Middle Earth, but the only beings that could possibly be his rivals would be either Smaug or the Balrog, and both of these were also servants of Morgoth long ago.
Though clearly, the ring itself seemed to strengthen the foundations of the black gate as well as of Barad-Dur to where they couldn't be broken down unless the ring itself was destroyed. Also, Sauron was able to turn all of Mordor into a black land, corrupting the very air itself, much like Morgoth did when he often corrupted the lands around him with his very presence. Sauron was also able to manipulate Mt. Doom and cause its poisonous fumes to spread out across the land into Gondor, blotting out the sun. Sauron was also a powerful sorcerer, and apparently both his Mouth and the Witch-King seem to have gained much of his knowledge of the craft.
Sauron was also the chief lieutenant of Morgoth, which placed him above the Balrogs and the dragons, and above Glaurung, Ancalagon, and Gothmog, the captain of the Balrogs. Naturally, he must have learned a tremendous deal of knowledge, crafts, lore of many things, and all manner of industry, construction, breeding, and corrupting of races from his time in service to Morgoth. The reality was that Sauron was so powerful and knowledgeable and wise, that he was the single greatest threat and embodiment of evil after Morgoth was defeated, all the way until the ring was destroyed. If Sauron had obtained the ring from Frodo, then all of creation, yes, Middle Earth and all the lands beyond that weren't part of Aman would eventually be conquered by Sauron.
If he had not died in Numenor and been able to escape the destruction, he would have been able to wipe out everything and he would have been the ruler of the world.
In my mind, Sauron and Eonwe were roughly equal. I do not think one could overcome the other in a one-on-one duel. While Eonwe was quoted as being "mightiest in arms", Sauron was said to be great in the lore of Aule's people and he had a host of other abilities as well. We do know Gandalf was the wisest Maiar. Also, like Eonwe, he served Manwe. It is not revealed how powerful he was before he was bound to his istari form.
Also, the ring did not make Sauron any more powerful than he originally was. The purpose of the one ring was to control the wearers of the other rings. Accordingly, Sauron had to pour the majority of his power into the one ring. Therefore, when he lost it, he lost a lot of his power. Getting the ring back would've restored him to his previous power level.
Additionally, it is not definitively stated who the most powerful Maiar were. We just know that Ilmare and Eonwe were the highest ranking. Of course, their rank would certainly lead you to believe that they were very powerful.
We are told that regarding the Valar, Melkor was the most powerful overall, followed by his brother Manwe. This does not mean they are necessarily significantly more powerful than the other Valar. Melkor feared Varda and Tulkas successfully defeats Melkor early on in the Silmarillion.
The point is these beings were all great in power and the only thing that we know for sure is that the Maiar were less powerful than the Valar. Tolkien explicitly explains this in the Sil.
Sorry but I have to correct a few said things. The ring did give Sauron more power than he otherwise would have had, 2 pieces of description tell us this; 1.It is told that the foundations of Barad-dur and the black gate was 'made' with the power of the ring, and so if the ring only gave him power over the other rings, he would have built his structures before he made the ring, and 2. If the ring gave Sauron no extra power other than control of the lesser rings, he would not have been as eager as he was to regain it, as he already had taken the 9 back from the wraiths and the 7 had been destroyed but for 1 and the 3 he would never have control over. Also remember Gandalf's words stating that destroying the ring had not even entered Saurons mind, so he was never worried about it's possible destruction, only someone else harnessing it.
As for any other being in middle earth that would be able to challenge Sauron,...Gandalf was able to take the life of the Ballrog (even though it cost him so much energy it took himself as well), no way would the ballrog or even Smaug be able to resist Sauron. Not just in battle, but Sauron would have enslaved them both to his will. Sauron was indeed the most powerful of the maiar and what made him excessively more powerful than any other being under the valar was the power he was given by Melkor. Remember the ballrogs were maiar too, so take the mightiest (Sauron) and add the extra might of power Morgoth passed on to him. Not more really need be questioned in regards to Saurons might and who would have been able to champion him. Glorfindel nor Gandalf could hold off the 9 all at once (and that's his wraiths without their rings on and him without the one). never mind Sauron himself. He was without question thee most powerful being in middle earth. You should also remember Gandalf's words that the power of the 9 would be tremendously increased if the one was back in Saurons hand, this is not simply because Sauron would have had more power over the rings, remember he already had complete control of the nazgul even though they no longer possesed their rings. Why would the Nazgul become so much more powerful if Sauron had the ring, he already had complete control over them, so it makes no sense to say they would be greatly empowered if Sauron had the ring, if it gave Sauron no extra power.