Competent - to me, a good villain is... good at being a villain. They make smart decisions, force the hero into good deals, and choose their goal over pointless evilness. They have control of their emotions, a long plan, and the brains and guts to do it.
Not every villain needs it. I have love for the villain helplessly pulled along by fate, or who is just too powerful for their own good, but, overall, I want a villain to be good at being a villain.
Too Real - Not always something I want, but I have a lot of respect for a villain that makes me uncomfortable. The kind of villain who reminds you of the worst people in your life, the people who made you feel helpless and scared, the kind of people who messed up your brain for years.
These ones are tricky. Kilgrave in Jessica Jones is a great example. He was deeply upsetting to watch because he was the epitome of a charismatic sexual abuser. In the wrong hands, he would have been a villain where lazy writers used rape to make him scary rather than making a genuine exploration of trauma.
True Believer - I really like villains who, to say the cliche, see themselves as heroes, especially ones who are just a breath away from the hero. Perhaps it's the Magneto type who thinks the hero plays it too safe and, for real justice, a few heads need to get bashed in. Sometimes it's the opposite, the villain who thinks the hero should keep their head down and play the game.
What's important to me with this villain is that they should be right sometimes. Whether they represent extremism or conformity, they should show the legitimate points of their viewpoint and feel like part of a discussion, not a forced moral.
A Dingus - Okay, I said I like real villains, competent villains, scary villains, but the world needs it's Doctor Doofinsmirchs. It needs the hammy villains who sing songs about their death rays, who attempt to flirt via lava lakes, who legally changed their middle name to evil and trip on their own shoelaces.
Also cold hearted ladies who aren't, like, femme fatale sexy. Competent, hard-working ladies who would watch the world burn for research data. Think Anna Ripley and Doc Oc(tavia)