Villain Ra's Al-Ghul has not only tried to be civil towards "the Detective", but has repeatedly offered Batman the chance to join his organization, and offered the hand of his beautiful (and mutually attracted) daughter, Talia.
A number of Ra's loyal League of Assassins members are also rather easy to get along with when they're not trying to kill you. This is especially true of Zedmore Washington, Prudence Wood, and Owens, which is probably why he sent them to try and convince Tim Drake to join forces with the League.
In Elseworld's Finest: Supergirl & Batgirl, Lex is a xenophobic, pitiless, egomaniac, manipulative, murderous, smug monster. He directly or indirectly murdered Supergirl's baby cousin and Batgirl's parents. However, he is always cool and polite. He even beams at you as he explains that he has been manipulating you all along and he is now going to kill you.
In H'el on Earth, H'el is rather nice to fellow Kryptonian, Supergirl, who also wants to return to her old life on Krypton. He later convinces her to join him in his quest to resurrect Krypton, but manipulates her to estrange her from Superman. H'el was also friendly to Superman, initially. When they first meet, H'el hugs Superman and even calls him his "little brother". Superman was already suspicious, but H'el threatening to snap Superboy's neck caused the two to become enemies. Ultimately he snaps and ends up as Faux Affably Evil, at best.
Otto Octavius, better known as Spider-Man's nemesis, Doctor Octopus, once rented a room from Aunt May, and behaved like a perfect gentleman, even helping her around the house. He also came very near to marrying her, after she somehow inherited a nuclear plant. May's inability to understand that he was a bad person was a running gag for a long while.
It became Faux Affably Evil during The Ends of the Earth and the following Superior Spider-Man arc.
And following Secret Wars (2015), he's pulled off an apparently genuine HeelFace Turn, even having a go at being Iron Man while Tony's out of action. Everyone is completely completely and utterly baffled by this.
Magneto, during Chris Claremont's first run, went from fantastic fascist to head of Xavier Institute to not quite back again, thanks in large part to his portrayal as an Affably Evil Well-Intentioned Extremist, to the point where his appearance at the end of Grant Morrison's New X-Men run which featured him putting humans into gas chambers and killing Jean out of spite was Retconned faster than a speeding bullet into being a lunatic called Xorn who masqueraded as him. Ever since, he's largely settled as the Good Is Not NiceFoil to the X-Men, willing to do the things that the more moral members baulk at (such as leading what is essentially the latest incarnation of X-Force as part of a long running habit of hunting down the enemies of mutantkind), and as one of their core members following the team's move to Utopia. At the moment, he's serving as The Mentor to the time travelling Original Five.
Also, Azazel. Apart from being the mutant equivalent of the Man of Wealth and Taste, he's shown to feel genuine affection (of a sort) towards Mystique and his son Nightcrawler.
Batroc the Leaper is a super-villain and mercenary, but is on Friendly Enemy terms with Captain America and temporarily reformed out of respect for Cap. When Ulysses Klaw hired him to help stage a coup of Wakanda, he still chided Rhino for needlessly killing an endangered black rhino. "We are guests in this country. It's just good manners."
The Mandarin has a heart of stone, but he is always impeccably polite and well-mannered. He also has a strict code of honor, which he always makes sure to uphold. He once vaporized his favorite minion on the spot for using poison in a sparring session, and he also upheld the promises he made on at least one occasion when Iron Man defeated him in fair combat, such as stopping his efforts to prevent Stark Enterprises from setting up in Hong Kong.
In The Secret Origin of Tony Stark, 451, the rogue Rigellian Recorder, is kind, friendly and really does want to help people, particularly humans and Earth. Even when Tony figures him out and snaps at him, repeatedly insulting him, he is still unfailingly polite. He's looking to guide the universe towards a peaceful future after seeing a highly altruistic species with almost no concept of warfare massacred for their pelts by the Skrulls. It's just that he's a Well-Intentioned Extremist writ large, believes that Utopia Justifies the Means and those means tend towards the incidentally genocidal - he doesn't want to hurt anyone, and he's genuinely remorseful when he does, but that doesn't mean that he won't if you can/do threaten his plans. And considering the scale of his plans, the length of time that he's been enacting them (500 years) and his requirements for those plans, this means that he has a kill count upwards of 40 million, including several species and at least two entire planets. After his plans hit a significant roadblock he was Out-Gambitted by Howard and Maria Stark, who raised their biological son, Arno, in secret, and adopted Tony as a decoy and he was faced with the possibility that it was All for Nothing he ended up in a Villainous BSoD and attempted a Heroic Sacrifice.
The Sleepwalker villain 8-Ball carries himself with a swaggering, casual manner. He is completely unfazed by the appearance of the bizarre alien Sleepwalker, and simply tries to smooth-talk Sleepy when he demands to know what 8-Ball and his gang are doing. He even cheerfully accepts Sleepwalker's claim of being an alien without blinking an eye, and kindly explains the Earthly concepts of money and power to Sleepwalker...before he attempts to murder Sleepy by dropping a bank vault on him.
Hoss, the redneck demon from Ghost Rider: Road to Damnation.
Thanos of Titan. The quintessential example of this aspect of his character would probably be the confrontation with the Gardener over his Time Gem: the entire incident consisted mainly of cordial conversation between the two as Thanos made a futile attempt at convincing the Gardener to willingly relinquish his Gem, with even the eventual fatal conclusion being devoid of malice from both sides.
Some of Thanos' conversations with Adam Warlock evoke this. Warlock is the only being to have peeked inside Thanos' soul, and so is perhaps the only one who understands him. When they talk to each other, they almost sound like friends.
The Serpent Society is a group of snake-themed supervillains with shades of this. In addition to members being friendly with one another, when one of them, Diamondback, semi-reformed, she also began datingCaptain America. Not only were her friends within the group supportive of her, but they also helped thwart other villains' attempts at ruining her first date with him.
ThugBoy and his crew early on. ThugBoy goes out of his way to ensure a hostage's comfort, and assures her that "This is business, not sadism, okay?" The leader, Frank, stays friends with ThugBoy even after trying to kill him for betraying the group, and gives him relationship advice.
Ninjette, who was originally hired to take out Empowered, but ended up becoming her best friend.
Manny, a Littlest Cancer Patient who wanted to be a supervillain. His Make A Wish is to tie up a superhero, but is incredibly polite and talks about how he researched how to do it effectively, but also without undue discomfort. He eventually takes a drug that makes him super-smart at the cost of vastly accelerating his cancer, and captures another villain with flesh-altering powers from Empowered, threatening her with several giant mechs while she is barely functional. But he's so darn polite, to the point of being nicer to her in their confrontation than most of her teammates are while working with her.
As can be seen from above, it's almost a bit of a theme that many of the villains are nicer to Empowered than her own teammates.
Gepetto in Fables. His kindly-old-grandfather manner isn't entirely a pose.
The Crypt Keeper, Vault Keeper, and Old Witch of EC comics were murderous ghouls, but remarkably personable and humourous.
Jeffrey Dahmer in the biographical My Friend Dahmer is a Real Life example. In high school, Dahmer became known as a Class Clown who had a fan club started in his honor after he pranked students and teachers with fake cerebral palsy fits. The author, Derf Backderf, drew humorous sketches of Dahmer for the school's yearbook and student elections. There is also a photo shown of Dahmer joking around at school.
Ozymandias in Watchmen. In addition to being a Well-Intentioned Extremist (on a par with Ra's al Ghul in that regard), he's also gentlemanly, witty, and calm, even in hand-to-hand combat. He treats his underlings kindly (right until he drugs them and leaves them to die of exposure to prevent his secrets from getting out, while apologizing for rewarding them so poorly). When his former crimefighting colleagues track him down and learn of his already-in-progress master plan, he gives them the opportunity to keep silent, and when all of them (except Rorschach) agree, he trusts them enough to not only let them live, but to offer them hospitality in his fortress and allow them to leave freely. Hardly seems fair to hold the deaths of millions of innocent people against him.
Mistress Ilsa from Monstress. A slave dealer whose specialty is Arcanic children, she is pretty unquestionably a villain. However, she isn't terrible about it. She lies to the children about their fate at the Cumaea compound (though that might have been to keep them from struggling), she offers Maika her cigarette in a small act of simple kindness, and when Maika is unchained and led into the Cumaea compound, she wishes her well and asks her to send her best to her daughter, who apparently she doubts she'll ever see again.
Lucifer from The Sandman and his own Spin-Off series is always polite and eloquent, even in his speech bubbles. He stops being evil by The Season of Mists, and settles for being a somewhat amoral Deadpan Snarker. ... and dives right back in to being evil in his solo series (the very first plot arc opens with him casually destroying another angel's several millennia of work over a mistake). He is still impeccably polite (until deliberately provoked), and always keeps his word.
Shade, the Changing Man encounters the "Devil", who comes across as a civilized, cultured gentleman who eventually stabs him in the back. He is Satan, after all.
Kathy: You haven't... given up your soul or anything? Shade: He's not interested in souls. And he's not really the Devil. And he's not as bad as you think. Quite easygoing, really.
Charon from Negation is the epitome of this trope. The cosmic-powered ruler of a universe-spanning empire that everyone lives in fear of acts like a laid-back, ridiculously mellow guy without a care in the world. Justified in that he purged himself of all his negative emotions eons ago.
Senator Greyshade in the first run of the Marvel Star Wars comics. One can picture him asking Darth Vader "Don't you ever have any FUN?"
Cap'n Blaze from Terry and the Pirates. He may be a warlord, but he is a jolly old soul who enjoys a game of checkers with his captives.
The Doll-Master from Wanted. He's a member of a supervillain Fraternity that rules the world. He's also a loving family man who never swears in front of children.
Transformers: Shattered Glass: Dirge is supposed to be a hero, but really works for Alpha Trion and his insane schemes for peace. This does not stop him from being cheery and polite, even to his prisoners.
Transformers: Wings of Honor: Portrays Runabout and Runamuck this way, despite being physically the oldest of most of their colleagues (who are teenagers, and quite nice themselves), act the youngest, explaining the war (and some deleted scenes) to Jhiaxus, with child like enthusiasm. They befriend an amnesic Side-burn, race with him, and give him dating advice.
Zero: Nova is a violent dangerous terrorist who is oddly polite and even affectionate to Edward. The effect is creepy.
Kroenen from Hellboy is a meek, polite fellow who goes out of his way to help his friends, even when he knows it'll get him in trouble. He's also a Nazi cyborg bent on destroying the world.
Diabolik and Eva Kant are unfailingly polite, calm and nice unless they need to be threatening (and sometimes they will be polite even then) or you earn their wrath, and are rather good with children. They also happen to be the world's greatest thief and scariest murderer and his partner in crime and lover, and each of them has a body count in the hundreds at least.