|Bad guys don't need to wear black.|
But then again, black can be awesome.
Easy, they're all bad guys.
What else to they have in common? While all villains in their respective stories, very little connects the three. Moriarty is a math professor gone bad, seemingly to start a criminal empire for the sake of it; an intellectual exercise for fun and profit. Sauron, of Lord of the Rings, is a being of pure evil who wants to conquer the word., with him as the only free person in it. Modred ... well, depending on what edition you're looking at, he's either a a pure tool of his mother, a weapon of evil, a manipulative little wretch, or, just guy who's gotten caught up in events that lead to a train wreck (for the last version, I highly recommend Mary Stewart's novels.... in fact, just read her. Now)
Creating a villain can be no different from creating every other character in a universe. A character is a character, and if you're trying to create a fully 3-Dimensional person on the page, it shouldn't matter if it's a protagonist or an antagonist. With Sauron, there is literally an entire backstory on him stretching back thousands of years (Tolkien, The Silmarillion); Modred was given a great deal of emotional and personal depth by Mary Stewart in her novels of King Arthur; and Moriarty ... well, he was a tool by Arthur Conan Doyle because he was tired of writing Sherlock Holmes, other people have stepped up to give Moriarty more of a back story, including Isaac Asimov.
In the case of my bad guys, I tend to have the history of not only the antagonist's parents, but their grandparents. They have hobbies and motivations and a history. They have back stories, and I could probably make books out of the bad guys I make ... but then again, the last bad guy as protagonist was probably The Talented Mr. Ripley.
However, there are schools of thought behind making villains. One is that "the villains really see themselves as the good guys; the heroes of their own stories."
My problem with that is that it presumes the villain cares about "right" and "wrong." Good, bad, they're the ones with the weapon. How many people honestly think Saddam Hussein believed that he was doing "the right thing"? Or maybe his ultra-violent, raping, torturing sons? The equally late and un-lamented Osama?
If you're thinking that "oh, all those people were sociopaths" -- who says? There are plenty of amoral little bastards out there. They don't think over morals, ethics, Nietzsche, the will to power ... though you'd be surprised how many think they are beyond good and evil.
This is my school of villainy. My bad guys don't care about what's right and wrong. They don't care about anything but what they want.
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And you don't need to be a sociopath to have a mindset geared towards "this is what I want," and "this is what's good for me," and screw the rest of the universe. If you have that type of a person, add together a total disregard for the consequences, and for anyone who gets in your way, you have a good, solid villain.
Could they have a code of honor and be a villain? Sure, why not? Honor is generally considered a system based solely on pride. And let's face it, when you amp "pride" up to eleven, you have the above parameters -- it's focused totally on "me."
And, no, a villain doesn't have to be pure evil -- torturing, sadistic rapist qualities are not a prerequisite. For some, not everything is about sex. And, hell, I live in New York, bondage and S&M is considered a subculture.
Hey, just because the character slashes someone's throat and watches their lifeblood coming out of them in spurts, chuckling manically, doesn't necessarily make them a bad guy. Though it could make them a fairly scary good guy? (If you ever get the chance, look up the first Mr. Moto film with Peter Lorrie. He plays a Japanese man in the 1930s, just as everything goes to Hell in the Pacific. You seem him kill people in what looks like cold blood. He always wears black gloves, black coats, and he always looks sinister. You have no idea what side he's on until the very end.)
On the other end of the equation, there are people who try to tell me that MacBeth was a tragic hero ... Really? That's like saying that all of the murderers caught by Columbo were heroes, as opposed to a murder mystery told from the killer's point of view. Here's a lesson to being a writer: if you're trying to make your hero tragic, don't give him a body count in the triple-digits that includes innocent women and children.
My point: you don't need a bad guy to be crazy for him to be evil. Nor do you need a sadist, a rapist, a pervert, sex-fiend, or Jack the Ripper.
The enemy in A Pius Man, for example, is none of these. Will he kill everyone in his way? Sure. Will he go out of his way to utterly and completely destroy thousands if he can? Absolutely. Will he rape, torture, and maim for fun and profit? No. Why? Because it's not efficient, a waste of time, and won't help him achieve his goals in the slightest.
And, for the record, to write an antagonist, you just need one person to have competing goals with your main character.
If you have a person with goals that run counter to the protagonist, then you have a good antagonist. What that antagonist does makes them a villain. For a bad guy, you need someone who must be stopped, one way or another.