Take it away, Stephen!
Regardless of how bad the bad guy is, sometimes the reader or viewer needs to sympathize with them. Perhaps they are a victim or in dire straits. Or they simply make unwise decisions. Example: John Q. A down-on-his luck father, whose insurance won't cover his son's heart transplant, takes the hospital's emergency room hostage until the doctors agree to perform the operation.
These characters are merely protecting what they hold near and dear to their heart. There could be an underlying moral or ethical value at the heart of the problem, one the reader or audience will need to consider as they watch events unfold before them. These villains are not pure evil, in contrast to The Joker or villains of James Bond movies who want to murder countless innocent lives or vie for world domination.
Perhaps the villain is being forced to do something terrible or else his wife and kids will be harmed, like Johnny Depp in Nick Of Time. His daughter is kidnapped and will be killed if he does not assassinate the governor of California.
Some villains are juxtaposed to the good guy, such as Ursula to the Little Mermaid. One is born into a royal family, one is born with nothing. Well, whoever said life is fair?
Then there are the mentally unstable villains who are not bad people to begin with. They just snap. Example: Michael Douglas in Falling Down who is having a really bad day. An unemployed defense worker frustrated with the various flaws he sees in society, begins to psychotically and violently lash out against them.
Then there is Carrie, a shy young girl who was picked on by the cool kids. She was a victim. She had telekinetic powers. She snapped. This is not going to end well.
Important: The villain often does not see themselves as a villain, such as vigilantes. Perhaps the police have failed to bring in a killer or the murderer has fallen through the cracks of justice. Vigilantes are people who do bad things but for seemingly the right reason. A villain may even be a delusional savior. The Twilight Zone has this theme in many of its episodes.
Which brings me to Dexter. But this is a blog all its own for next week.