Okay, so this could get a little long.
For starters, there are indications Sauron wasn't quite a full-powered Ainur as he had been before he tied himself to Morgoth, specifically in that there were issues with him just tossing around power or creating things. Like the Balrogs, he was cut off from Ilúvatar; like Morgoth, great expenditures of power would diminish him because he would need to put some of his own power into his creations. This was (one of) the reason he went with making the Ring - by putting his own power into the Ring, he could then wield that power without fear of it diminishing, in order to control and dominate (it also gave him power over the other Rings in a direct way, which ties into his need/desire to control and dominate other races - take control of the leaders, control the race), or make things (he laid the foundations of Barad-dűr with the Ring's power, tying them to the Ring...cost him nothing, and they would endure as long as the Ring endured). It also made an anchor for him; if his body were slain, so long as the Ring existed it would hold his power and he'd be cool.
He was smarter than Morgoth in that respect, Morgoth being a guy who (especially in Tolkien's reimagining of his work) peed all over the world in order to corrupt it and mark it as his territory, and squandered a chunk of his power in the doing.
And Sauron discovered back in the First Age he could be beaten. Lúthien and Huan demonstrated that rather dramatically, back when Sauron still had the guts to try to do the work himself. THEN he got to watch the Armies of the West show up and absolutely kick all hell out of Morgoth's supposedly unbeatable forces. He was forced to surrender and beg Eöwnë for mercy.
Then he runs into the Númenoreans (for like, the second time, they've already helped wreck his armies once), and their armies are so huge he realizes his forces can't win against them, and he really, really doesn't want to fight them personally; if his own forces get wiped out, how's he going to rule? And it's perfectly possible for him to get beaten -- I mean, Númenoreans have stuff like Narsil, First Age weapons, and are perfectly capable of making other things that we would consider 'magic' (Merry and Pippen's blades, for example). Also, Sauron is more of a schemer and controller than a being like a Balrog that runs around beating people over the head with a flaming sword, and he sees a chance to corrupt Númenor for his own purposes, the easy way (from within).
This isn't conjecture on my part - I'm laying a foundation to make a point, it'll be backed up by stuff from the books.
Then Númenor gets annihilated, his body is slain, he's forced to float his incorporeal ass back to Mordor and make himself a new body. And he loses the ability to take on a fair form. Forever. Bit of a shocker, I imagine.
Then comes the War of the Last Alliance.
Sauron does NOT want to take the field. This is explicit in the writing. He's not feeling terribly confident in the situation, there are First Age Elves out there with First Age weapons, there are Númenorean heroes...he eventually comes out after a seven-year siege when it becomes clear that things are all-but lost for his forces.
He gets killed.
Without the Ring, he then is forced to spend a HUGE amount of time creating a new body, and then even more time getting his power back. This is the part noted in Lord of the Rings, in The Council of Elrond, where it's pointed out that Sauron's big failure this time is being TOO cautious. His enemies are only a shadow of what they used to be: the power of Númenor is utterly broken (by late Third Age, with Arnor destroyed thanks to his machinations and Gondor weakened by the same), and the Eldar are weaker than they ever have been. But still, having suffered failure after failure, and loss after loss, AND not having his Ring, he's overly cautious (it's a thing in Tolkien that evil eventually becomes craven, because it worries only about itself). He moves too slowly. If Sauron had started up a blitz at this point, he likely would have simply rolled over Gondor (as he was doing in Return of the King) and then...maaan, who is left? Galadriel can't take on an army of 100K orcs herself while they're burning down Lothlórien around her. Imladris really has no 'army'. Rohan would be nothing to Sauron, all by itself. He already has Umbar/Harad and the East. What's left? The Rangers?
But no, he doesn't. Basically, Sauron has become afraid.
Monstering around Middle Earth as a dark lord doesn't give him the power to RULE it - he needs to take and hold - and exposes him, again, to failure and potentially getting diminished again for a long period of time (if it comes to a personal fight, there's still the White Council to deal with, and they're not exactly a bunch of wimps). Without his Ring. Then there's stuff like Aragorn seizing control of the Palantir from him and waving Narsil reforged in his face ('Hey, remember this?') to stress him out.
There's also the vague risk of the Valar doing something. I mean, last time Sauron got personally involved and started shooting his mouth off at the Valar, Ilúvatar kind of broke the world. Sauron doesn't 100% KNOW that the Valar won't send over Tulkas to kick his ugly butt if he starts stomping around like mini-Godzilla. <-- THIS part is conjecture; maybe Sauron knew full-well the Valar wouldn't get 100% involved any more, I don't know, but if it were me I'd be worried about Tulkas doing the Kool-Aid Man thing on my front gates.
But WITH the Ring? He's not so worried any more (not about the Valar, mind, but other things). Getting killed suddenly seems ridiculously unlikely with his enhanced power.
I will grant that it's possible Sauron isn't yet at his best in Lord of the Rings, but we don't really have any real idea where he stands at that point. *shrugs*
Okay, now on to power levels.
Tolkien on the subject of Sauron and his Ring, from Letter 131.
Basically, Sauron without his Ring is still essentially doing fine. The reason he's slowly gaining power through thousands of years before Lord of the Rings, and only feels confident enough to openly declare himself in the final century before the story starts, is because he was horribly weakened by being 'killed' and not having his Ring with him to assist putting Humpty back together again. ^_^ Also sadly lacking in 'gigantic armies'.Originally Posted by Tolkien
Again, has he gotten the gas tank back to 'Full' by the time of Lord of the Rings? Good question. But it's interesting to note that he's perfectly capable of exerting his will over an army of his servants over a great distance.
Edit: the above quote points out another reason why Sauron wouldn't want to take the field, himself. He doesn't know where his Ring is. It's not destroyed, but ANYONE could have it. If he takes the field, and then Galadriel shows up wearing HIS Ring, and with the White Council behind her...that's a big problem. He'd much rather have any Ringbearer declare themselves while he's safely hiding in Barad-Dűr, and can send an army to crush them.
Tolkien himself was pretty clear (again, Letter) that Gandalf the White was the only person who could managed to master the Ring then defeat Sauron, but Sauron is plauged by doubt and isn't the writer of the story; for all he knows, Galadriel, Saruman, or some other luminary could manage it.