Sauron is that all-mighty evil nasty thing that made the One Ring? Please. He's a skinny cowardly freakazoid beeyotch compared to Melkor.
Melkor was Tolkien's biggest-baddie of them all. How do we know? He created Balrogs.
In J.R.R. Tolkien's universe, spiritual entities are called Ainur. The Valar are the most powerful of these, essentially a form of archangel. There are 15 of them -- with Manwë, a male Valar, being the most powerful. But Melkor was equally powerful to Manwë, if not even more so. Iluvatar ("God" in Tolkien's world) asked his Valar to help him "sing the world into existence". (Singing the world into existence is a common creation myth.) Melkor, however, didn't want to sing the same song as everyone else, so he introduced evil into the world by singing a different song. Some things he created were new and wrong; other things were twisted versions of goodness or beauty.
Lesser Ainur are called Maiar. These are animist spirits -- the spirit of the lake, the spirit of the hill, the spirit of the valley, the spirit of the tree or the deer. There are bazillions of Maiar, some more powerful than others, but all of them dedicated to a single place, species, thing, or idea. The wizards -- Gandalf, Saruman, Radagast, and others -- were all Maiar, although they were the most powerful Maiar around. Sauron? Just a Maiar!!!! A very powerful one, but nothing more than your common squirrel-spirit or shrub-ghost.*
As the song went on, and then once it was over, Melkor kept sneaking into Middle-earth to do even more damage, most of which wasn't apparent to the Valar for millennia. He built two, vast fortresses in the arctic: Angband, his greatest work (delved so deep into the earth that its dungeons, pits, and hell-holes are unnumbered), and Utumno, a smaller version of Angband that served as a watchpost. Melkor destroyed the Valar's home in Middle-earth, forcing them to create and move to Valinor, a mystical isle beyond the western sea. There they created Two Trees to give light to the world (as the sun and moon didn't exist yet). Melkor was captured in the "War of the Powers" and chained for a thousand years. He then convinced Manwë (who is kind of stupid) that he had reformed. He destroyed the Valar's home again, fled to Middle-earth with the Silmarils (Elvish jewels which captured the light of the Two Trees), and started doing more evil.
It's about this time that Melkor creates a bunch of things. Among them are orcs (Elves which are tortured, twisted, and corrupted into a race of pure evil), dragons (unfortunately, it takes hundreds of years for their skin to harden, so they don't appear on the scene very quickly), and Balrogs.
Tolkien's concept of the Balrog changed over time. He initially indicated they were pure creations of Melkor, like dragons. In his later writings, he seemed to think they were fire-Maiar. Like orcs, Melkor (who the Elves called "Morgoth", or "the enemy") twisted the Balrogs into evil things. But unlike orcs, the Balrogs apparently underwent this process willingly.
How many were there? In The Silmarillion, Tolkien's history of Middle-earth, there are THOUSANDS. They are only twice the height of a man, and rode dragons into battle. They were hot as lava, and just being nearing them could burn a man severely. They had whips (it's not clear if they were physical, or made of fire, or on fire), swords, axes, maces, and claws like steel. They sometimes wore chain-mail, and were very strong. Yet, holding them under water (and dousing their heat) could kill them, and if you pumped enough arrows into them or slashed them enough with swords, they could die.
But The Silmarillion was not fully finished by Tolkien. In The Lord of the Rings, which was finished, Balrogs are FAR more larger and powerful. Tolkien apparently contemplated reducing their number, too, so that there were only seven (this never made it into the LOTR text, however).
Interestingly, Tolkien seemed to abandon this idea after LOTR was published, and in drafts of his later writings he returns to the idea that there were thousands of them.
What did Balrogs look like? That's hard to say. They were dark, and had cracks all over their body through which red fire gleamed. Now, Maiar are spirits, and not physical beings. They can take on physical form; indeed, hurt a Maiar enough, and they lose the ability to choose certain forms. (Sauron, for example, was once able to take the form of a handsome man. After causing the downfall of Númenor, however, he lost this ability.)
In The Lord of the Rings, Tolkien provides the most complete description of a Balrog Yet: It appeared "like a great shadow, in the middle of which was a dark form, of man-shape maybe, yet greater". Tolkien says the Balrog actually passed through the Dwarf-sized door to enter the chamber of Mazarbul (where Balin's tomb was). But just a few pages later, while in the 21st Hall, it "drew itself to a great height, and its wings spread from wall to wall". Given how vast the 21st Hall is, the Balrog would need to be enormous!!! (In an early draft of The Lord of the Rings, Tolkien said the Balrog was man-high, with fiery eyes, long arms, and a red tongue.)
Whether Balrogs have wings is also unclear. In The Lord of the Rings, Tolkien wrote, "His enemy halted again, facing him, and the shadow about it reached out like two vast wings." Oh, so they're only shadows. BUT WAIT! "...suddenly it drew itself up to a great height, and its wings spread from wall to wall..." Oh, so they ARE physical wings.
Frankly, Virginia, Tolkien just isn't clear on the subject.
Even the way you kill a Balrog changed. The Silmarillion is quite clear you can douse or drown them. But Gandalf and the Balrog fall into a subterranean lake beneath Moria. The Balrog survives, although its form is now slimey and mud-like. (Maybe he didn't hold it under long enough?) Gandalf continued to hew at the monster with his Elvish sword, Glamdring.** The Balrog fled, and Gandalf pursued it for eight days up the Endless Stairs. They emerged on the mountaintop, where he finally killed the creature (although he died himself in the process).
Here are depictions of the Balrog. Three are from John Howe, the British painter who has done hundreds of LOTR and Hobbit paintings. You can see how different each one is. (One depicts the Elf, Glorfindel, defending Gondolin from a Balrog.) Howe later did the artwork which Peter Jackson used for his films, and that's yet ANOTHER conception of what it looked like. One of the images is by the Brothers Hildebrandt, traditionalist fantasy painters working in the 1970s and 1980s. Two images are from the Jackson movie.
* - If you wonder why Gandalf et al. couldn't defeat Sauron easily, you're in good company. Tolkien suggested in his letters to friends that it's because the Valar wanted Men, Elves, and Dwarves to do so; thus, Gandalf et al. agreed not to use their Maiar powers while in Middle-earth. Sauron, however, was under not such compulsion. This still begs the question, however, and Tolkien never really provided a good answer except "That's the story I wanted to tell".
** - Glamdring was forged by the Elf Turgon. Turgon was one of the Noldor, those Elves who swore a magical oath to retrieve the Silmarils from Melkor or die trying. But once in Middle-earth, he became worried that the Elves would lose. So he quit the battle, and after some years discovered a hidden valley ringed by high mountains. It could only be reached by an underground river (now long-dry), and thus was nearly impossible to find. He led his sub-tribe of Elves there, and they established the magnificent walled city of Gondolin. Gondolin would later be betrayed by Turgon's nephew, the evil Elf named Maeglin. (Yes, there are evil Elves!!) This sets in motion a long chain of events that leads to the defeat of Melkor, the birth of Elrond the Half-Elven, the rise of Sauron to replace Melkor, and much more!! Glamdring was rescued from Gondolin by the human named Tuor (Turgon's best friend). Tuor's daughter would marry an Elf, and their sons are Elros and Elrond. Elros decided to emphasize his human side, married a human woman, and his great-great-great-great-great-great-Nth-great grandson is Aragorn. His brother is Elrond, who decided to emphasize his Elvish side. Essentially, Elrond's daughter, Arwen, marries her cousin. EWWWWW!!!!