John Kramer/The Jigsaw Killer - SAW
The most compelling villains act in a way that they honestly believe that they are right. Pure evil doesn't tend to exist, more a justified darkness. John Kramer, in his guise as the Jigsaw Killer in SAW, is the classic example of this. Placing his victims in games that require them to prove their commitment to staying alive, his justification is an perverse mix of divine calling and 'they've got it coming'. Over the course of seven movies, we see how he goes from vengeful victim to sadistic sage. By the end of the saga, you're not sure if he was the protagonist or antagonist of the story but you find yourself oddly rooting for him.
Darth Vader - STAR WARS
Ironically, when provided with his backstory, he becomes a less effective villain. When we had just the original trilogy, we accept that he is just evil. Because it is in a science fiction, we can accept that he is ruthless and vicious. The outfit and the execution is done so clinically that the terrifying thing is the absence of emotion. His absence of humanity means he will kill his troops just as readily as he will his enemies. It is science fiction's answer to Genghis Khan.
The Joker - THE DARK KNIGHT
Chaos is a terrifying thing because it plays on the most primal fears of human nature. Heath Ledger's Joker personifies this fear by using perceived chaos to gnaw at it. However, chaos is the title the Joker gives to his very organised attack. He claims to not have a plan but he clearly does. He is not an idiot but he is hugely unpredictable. This is portrayed perfectly when he gets captured and then uses it to his advantage by bringing Gotham and Batman to their knees. It is so audacious that it has become something of a template for villains now.
Bane - THE DARK KNIGHT RISES
Bane is actually scarier than the Joker. He's not as haunting but what he represents is far scarier. Bane is a symbol of how dictators rise to power. He uses menace and fear to initially control the people and over time slowly corrupts them to his way of thinking. He is a demagogue, appealing to people's sense of injustice and twisting them until their darkest desires masquerade as pure motives. While the Joker took Gotham to the brink, Bane drags them clean over it and Gotham unnervingly accepts it. It is the superhero movie's answer to Hitler and Stalin.
Clyde Shelton - LAW ABIDING CITIZEN
Those who have seen this movie will argue whether Clyde is actually a villain. I understand because I found myself rooting for him too. It is the reaction we'd all want to do if put into his shoes. After surviving a home attack that saw his daughter and wife raped and murdered, Clyde sees the worst of his assailants get off with a light sentence. Infuriated by a legal system that takes the easy conviction, he goes on the warpath but one that is carefully calculated over the course of ten years. When he strikes, his revenge is planned, brutal and satisfying in a viscerally disturbing way. As he kills everyone involved in the injustice, we marvel at his ingenuity to keep on killing despite his incarceration. He represents the primal craving in each of us to have revenge and how once it is unleashed, it will not stop.