Not entirely, though. Villains seem to be the characters of the day - or month - and when Georgie and Sky released their Villain edition of Beautiful people in May, my mind soon went to a line from one of the Midsomer episodes. I can no longer remember the exact quote, and I've no intention of trawling through fifteen seasons' worth of episodes to find it; but in the main, the detective was asking another character if he knew about the trinity of murder. That is,
Three things that seem to me fitting questions to ask any villain, murderer or not. After all, there is an art to creating a memorable villain, as much as there is an art to creating a (hopefully still more memorable) hero; greatly as a billowing black cape may enhance the awfulness of any antagonist, it is, alas, not the deciding factor of villainy. So what about this trinity?
Much is written about backstory - the primary factor in forming any character's motive, including that of the villain. He must have some reason for doing what he does, or he will only come across as arbitrary and irritating. Writers are forced to take into account that, depraved though human nature is, it is still considered unnatural to commit certain crimes, including murder; one usually doesn't simply wake up one morning and decide to take a jaunt before breakfast to kill a handful of people. An impetus is needed. What is that happened, or is happening, in the villain's life that set him on this particular path?
That said, I'll add that it isn't necessary for the villain's backstory to overwhelm the story, or even to be worth sympathizing with. I never sympathized with Wickham, or Magua, and I've only ever remotely sympathized with one of my own villains. Some people are just plain wicked, and it takes a great deal of effort to summon up any charitable feelings toward them - especially if they're on a page. But you know, even psychopaths use a form of reasoning, and it ought to be lightly threaded into the story.
Another thing to consider in the search for motive is that the external impetus is not enough. Two people will react to an event in two different ways. One character may suffer poverty and come out on the other side with more charity and compassion; another may become Ebeneezer Scrooge. The mental configuration of the villain is even more important than the outside events one may lob at him, for abuse and rejection and poverty and starvation and the whole shebang will only warp a character as much as he allows himself to be warped.
The villain has to spend most of the story with opportunity, and greater opportunity than the protagonist. The story will always be a give-and-take between the two characters, a battle in which sometimes one side and sometimes the other will come out the victor. But for the most part it should be the villain who keeps the upper hand, for otherwise he isn't much of a villain at all. The greater the villain's success, the greater the tension. Thus, he must be in a suitable position for whatever it is he is attempting to do - or he must have good connections. Good connections are always to be coveted. (Although one must take into account that if one wants a thing done properly, one has to do it oneself. Never trust matters to the hired help. Important advice for those who are considering ruling the world.)
Here there is a great deal of room in which to play. The usual fallback means for villains to get what they want tends to be murder, but as mentioned above, that is hardly what one would call a "natural" thing to do. The character has to be pushed very far, and have a certain makeup, to resort to that. So before pinning the murder on him, the writer has to stop and consider whether he is in fact the sort of person to bring about his own ends by taking another person's life.
If not, there are other means, just as wicked, some more insidious, that don't require any physical blood being spilled. Manipulation is a good example and can take any number of forms, including blackmail; bullying also works, especially for characters who are rather childish. For stories set in fantastical worlds, sorcery presents a whole array of possibilities. And in any genre, there will be those villains who prefer to work entirely behind the scenes, pulling the strings so that others do the work for them. In this instance, however, it is important to know why the puppets agreed to being on the strings in the first place...
...and then you go full circle and are back to "motive" again.