Nurgle, the Chaos god of disease, decay, despair, and destruction is a jovial, avuncular figure who lavishes attention on his "children" and sees himself as a creative force in the universe. He is often referred to as Grandfather Nurgle, or even Papa Nurgle. The same can be said for his mortal followers. In the fluff, you'll almost always see them joking or having a good time. At one point, after a POW gave up and agreed to worship Nurgle, his jailer just smiled and hugged him. Black Crusade makes Nurgle even more affable by explaining that his role in the cosmic scheme of things is as the "Celestial Janitor" for the Eternal Recurrence; he's the guy who breaks down the ruins of the old and the corrupt after their decay generates the daemons of Chaos in the first place, creating the fertile loam from which new, purer life will spring in turn. And, given the Crapsack World nature of the setting, it's very hard to argue with his stance that the current galaxy is well past the point where he should be euthanizing it and composting it.
Also Trazyn the Infinite, a Necron lord who collects various treasures throughout the galaxy. He could not care less about conquering anything, unlike most other Necrons, and generally has the demeanor of a jovial elderly man who owns a toy store. At one point, he was attacked by a few Imperial Guard platoons. He later sent a message to their commander stating that while they put up some unnecessary resistance during the transaction, he was genuinely grateful that he received the last few specimens he needed to complete his 'Guard platoon' collection (as what he presumed were gifts).
Another Necron is Nemesor Zahndrekh who was damaged during the Necrons' Great Sleep, making him a bit... odd. Mostly he just acts like a slightly senile and idealistic general who thinks he's still Necrontyr, and as such only employs honorable methods of warfare. He's also probably the only person in the galaxy to routinely take prisoners and is not trying to convert them (Tau) or execute them horribly (everyone else), preferring to show them the wonders of Necrontyr technology and generally act as polite and civil a host as can be, much to the irritation of his (lucid) Necron Lords. That said, this is less him being a nice guy and more the robo-Alzheimer's making him think he's fighting other Necrontyr during their Wars of Secession. Fortunately for him he's still a military genius and his old man ramblings about wars long past are somehow still completely relevant to the situation, meaning that as much as his cheerful personality and honorable streak piss off his fellow evil robot skeletons, he's too useful to kill.
The bread and butter of both World Of Darkness gamelines by White Wolf.
New World of Darkness: This is especially common in the Vampire: The Requiem gameline. Since vampires are evil within the context of mundane human in-game morality, they do what they can to prevent themselves from appearing evil. The Ventrue and the Daeva clans, particularly, thrive on this trope, even going so far as to have an active rivalry between each other as to which style of manipulation (Honey vs. Vinegar) is superior. Unlike their Masquerade counterparts, the Nosferatu of Requiem can also handily play within this trope, and can even outdo their classier and prettier opponents.
In the Mekhet clanbook, Frances is funny, sweet, apologetic, and into indie music. She also brainwashes a house full of female students so she can feed on them, turns her boyfriend into her devoted ghoul ("I think I've broken him"), and toys with a female executive before killing her in the most humiliating way possible.
Forgotten Realms has Sshamath — technically, it's an evil drow magocracy, and they didn't disown Lolth, having only thrown off the theocracy. But for the sake of trade, it was made as pleasant as a drow city could be. This includes restrictions on slavery and having one of the best taverns catering to any sentient being (with special floors for freshwater, saltwater, and flame-dwelling clients).
Dragonlance: Some of the Krynnish evil deities can be very friendly when they want to be. Sargonnas really does care about his followers, and has standards and a sense of honor. Nuitari can get along well with Solinari and Lunitari, due to the three deities representing Evil, Good, and Neutral magic. He also can get along fairly well with mortals. Chemosh, the God of Undead, is apparently capable of caring enough for another being that he can feel genuine grief when that being is hurt. Zeboim, the Goddess of Storms, really does care for her son. In terms of mortals, the Black Robes frequently come across as being rather nice (Dalamar and Iolanthe) and are able to get along with their White and Red Robed fellow Wizards.
In the Planescape campaign there's the half-demon wise-man Rule-of-Three, named for the axiom of the same name, who sells information about demons and the Abyss in Sigil. If you can get past the fact that he's a demon, he's a pretty decent sort. (There are some pretty unpleasant rumors about how he gets his information, and his detractors tend to disappear before they can prove anything.) Almost nobody knows that he works for the demon lord Graz'zt, the second most powerful - or third, depending on who you're talking to - ruler in the Abyss, who can also fit this Trope if he wants to; well, he's likely the closest to this Trope a demon lord can get.
Elesh Norn from New Phyrexia storyline is the fanatical leader of Machine Orthodoxy, a faction that sees flaying as the first step to perfection. However, she's also very charismatic and motherly (for Phyrexian standards, at least), and is in very good terms with the blue Praetor Jin-Gitaxias. She's depicted in cards as serene and poised.
Nobilis: In third edition, Hell sincerely loves you, and everything else in existence, but has spent so long focusing its love on the corrupt and malignant that there's been a degree of cross-contamination. The Excrucians can also come across as charming and caring yet a horrifying threat to all of existence.
In the spinoff Chuubo's Marvelous Wish-Granting Engine, there's the Headmaster of the Bleak Academy. The Bleak Academy is an Academy of Evil that hungers to unmake the world, which has "your hopes are dead" on the Properties list for its gates, which sits in the space where a heavenly afterlife could be, and which trains its students to wage war on existence itself. One Kickstarter freebie detailed the Headmaster and the author of the game, Jenna Morannote who writes most of her Nobilis 3e/Chuubo stuff as though she was present in the setting, striking up a strange friendship while doing their laundry in Fortitude; his stats include Compassion 3, Philosopher 3 and Teacher 1; and apart from that time he killed the old sun, most of what he does seems to be serving as a psychopomp rather than as the enemy of the world.
Exalted: The ideal for Moonshadow Caste Abyssals is to be an approachable, sociable diplomat for the faction that wants to drag all of Creation into the Void at the bottom of the Underworld. But really, anyone with high social skills and goals that are opposed to yours can come across as this.
Ligier, the Green Sun, is the fetich soul of Malfeas, the fallen King of the Primordials, effectively making him the crown prince of Hell. He's also a massive egomaniac, to the point where his Motivation and Intimacies are all focused on himself and things he's made. At the same time, though, he's also calm, restrained, and courteous almost to a fault, to the point where if someone can get a lucky hit on him in battle, he'll compliment them on their skill and leave peacefully.