"Bad man. Good manners."
—Ron Stoppable referring to Señor Senior, Senior on Kim Possible
Most of the time, when there is a Villain, they're going to have a personality or manner that underscores how evil they are. They may kick puppies for giggles, be particularly insensitive, even during sex, or might just be too unknowable to be anything but evil.
And then, there are villains who are Affably Evil. There is absolutely nothing separating them from being normal, polite people except for the fact that they want to Take Over the World or use human souls to power their Artifact of Doom. They're not the Stepford Smiler—their affability is a genuine part of their personality, not a mask. If they have underlings, expect them to be a Benevolent Boss. In one way, they're the opposite of an Anti-Hero. They may Pet the Dog on occasion, but won't hesitate to kick it with steel-toed boots the next second if it helps them accomplish their goals. They may well be a Villain with Good Publicity.
This villain will invite the hero out to tea, offer him a favorite dish, make pleasant small talk, try to appeal to the hero's better nature, and convince the heroes that the villain's plan isn't worth getting involved in. Of course, if the hero still won't change their mind, the villain will remind them that they are, after all, still a villain. It may or may not involve a Death Trap, depending on how nice the villain really is when crossed. Of course, inviting the hero's mom out to tea might send a stronger message. The friendliness of said villains can serve to humanize these guys.
Almost always either comedic, or a charismatic Magnificent Bastard, or a Well-Intentioned Extremist who really believes that they are the good guys, but the occasional Complete Monster can exhibit such qualities as well. Evil Has a Bad Sense of Humor is not true for them, and their affability even makes them easy to "compliment" with an Insult Backfire. Captives of an affably evil villain won't be kept in dungeons, but in a Gilded Cage.
Please note, in the event an Affably Evil villain does undergo a Villainous Breakdown, the very traits that make them so pleasant often serve to make their breakdown extremely creepy or outright scary. A kind, friendly man suddenly going into a psychotic rage is made all the more scary by the simple fact that he was previously so nice and kind. If they keep their inviting personality while going utterly Ax Crazy, it makes them seem downright creepy and disturbing.
- Punch Clock Villain, who isn't necessarily evil at all—they simply have a job to do, and if that job involves slaughtering innocent children or stealing people's life savings, well, that's what they get paid for.
- Villains Out Shopping for Affably Evil behavior in otherwise normal villains. Often a trait of a Card-Carrying Villain, especially in the more ironic portrayals.
- Villain with Good Publicity. This trope may be the reason WHY he is so popular with common people.
- Faux Affably Evil, which is a villain who adopts an affable demeanor that isn't genuine, basically mocking Affably Evil.
- Freaky Fashion, Mild Mind.
- Bitch in Sheep's Clothing, where the character hides a more sinister side behind a nice facade—unlike them, Affably Evil characters are genuinely nice.
- Harmless Villain, when the villain is only affable, without the actual Evil part.
Good Is Not Nice is the good(ish) Sister Trope, and such good guys are particularly good at giving the Affably Evil a proverbial punch in the nose. I'm Not Hungry is often dealing with this villain. A villain will often engage in Too Funny to Be Evil to achieve this effect.
No real life examples, please; absolute values like good and evil are best kept away from the complex spectrum that is real life. In the case of people widely regarded as evil, we want to avoid arguments over whether to classify them as True Affably Evil and Faux Affably Evil.