The Cybermen are this from "Revenge of the Cybermen" onwards until the end of the Classic series — once emotionless robots now portrayed with limp wrists, lisping voices and hilariously horrible amounts of mincing. Not helped by the tight silver bodysuits and the Doctor pointing out they get killed with "glitterguns" — a bit Disco even by the standards of an episode from 1974.
Mehendri Solon in "The Brain of Morbius" wears a lot of fancy jewellery, is hugely misogynistic, spends his time making 'models' of striking male faces and appears to find the Doctor very attractive (attractive enough to want to steal his head for a horrible Frankenstein's Monster, at any rate), even flirting with him in some scenes as much as 1975 would allow. Note the models resemble Classical sculpture and Solon is the name of an ancient Greek politician.
Mad gardener Harrison Chase in "The Seeds of Doom" is camp, fey, fastidious, Wicked Cultured, wears fashionable clothes and black leather gloves and 'could play all day in [his] green cathedral'. He also ties men down, forcibly converts them into plants, and then brings them plant food (chunks of raw meat) to eat while they're in bed.
One of the flaws Douglas Adams noted about his script for "Shada", which he strongly disliked, was that he'd written the villain Skagra in this way, which he admitted was lazy on his part and neither funny nor frightening, especially in comparison to the dynamic and interesting villains in his much-preferred script "City of Death". He is Rescued from the Scrappy Heap in both the Big Finish adaptation (in which he gets a ridiculously hammy performance from Andrew Sachs) and the 2012 novelization, which makes him androgynous and unexpressive as well as fleshing out his backstory and personality a lot.
Turlough is introduced in a public school (and keeps the uniform), an aesthete, and his darkness is portrayed as him being sensitive, fey and cowardly. He does do a Heel–Face Turn, though, and keeps up the camp.
The Master often gets into this, from his Foe Romance Subtext with the Doctor to his often-ostentatious outfits such as the velvet blazer and ruffled shirt he wore in Anthony Ainley's incarnation. Exaggerated with Eric Roberts' depiction in the made for TV movie in which he's swishier than Cruella De Vil, wears a leather jacket and later Cuban heels with a glitzy Time Lord robe, striking a melodramatic pose worthy of Ratigan or Frank N. Further and claiming "I always drezz ... for the occasion." John Simm's Master gives Roberts a run for his money, prancing, flouncing, dancing to popular music as he conquers the Earth and exercises his tyranny over the population, blowing kisses and flirting with the Doctor like there's no tomorrow. However, he also has a beautiful wife and comes across as quite homophobic in addition to his misogyny and racism.
Game of Thrones: The eunuch Lord Varys subverts this trope brilliantly. Really, when everyone already knows you're a eunuch, what the devil's the point of wasting time embarrassing yourself by trying to look butch? Raised by actors, he knows how to play the role properly to keep the Queen and her council guessing. Even Magnificent Bastard Petyr Baelish doesn't quite know what he's up to. It's mostly an act—when he gets truly angry or serious he drops his usual polite, facetious tone and his voice becomes considerably lower, first seen when he delivers quite a hardass What the Hell, Hero? to Ned Stark when trying to convince him to give a false confession and demands him to serve the realm, or when he threatens Tyrion in Season 2 and Littlefinger in Season 3.
Cobblepot is more than a little fey on Gotham and sometimes attempts to be flirtatious with Gordon. He's prissy, sycophantic, and loves his formal wear...and a manipulative, ruthless killer.
Averted in Kings. Prince Jack is both a homosexual and a villain but he's also a soldier who commands the respect of his men and is fully capable beating a guy to a pulp in a bar brawl.
Although he's definitely heterosexual, as far as mannerisms go Chancellor Dongalor in Kröd Mändoon and the Flaming Sword of Fire practically floats out the window. Considering how snarky he is about the actual gays in the show you have to wonder what he's repressing.
And of course he's played by an openly gay actor.
A Law & Order: Criminal Intent episode gives us Dr. Roger Stern, a prissy, cultured surgeon who is well aware that he's prissy and compensates by doing terrible things to women.
Meemy or thereabouts from Mahou Sentai Magiranger. Imperious from Power Rangers Mystic Force was less so, though little attempt was made to hide the mannerisms (reminiscent of Queen Machina, actually) and when he first took that form, he called it "beautiful." Both versions are pretty non-flirtatious, though, and certifiably able to reduce you to very small smithereens.
One Monster of the Week called the Octophantom didn't look very feminine, but he certainly acted that way. He was so vain that Billy was able to distract him by getting him to pause - mid-battle, no less - to admire himself in a mirror, and enable the heroes to gain the drop on him.
An even more egregious example is Flame Head, a fire-themed monster with what sounds like an obviously female voice and feminine mannerisms, but is actually male.
Stag Beetle after the Megazord chops off his pincers.
MY BEAUTIFUL PINCERS!
Parodied in an episode of Monty Python's Flying Circus, involving Special Investigator Lemming of the British Dental Association. Mad Dentist Super Villain "The Big Cheese" is played by Graham Chapman in one of his more flamboyant performances.
Flopsy's dead and never called me 'mother'.
Murdoch Mysteries: James Gillies is a recurring villain who murders people For the Evulz (and later to get revenge) and to prove that he's smarter than Detective William Murdoch. He's somewhat effeminate, soft-spoken, occasionally wears women's clothes (he did it to disguise himself first, but later admits he likes it), and he used dolls in one of his schemes.
Rumpelstiltskin (portrayed by Robert Carlyle) in Once Upon a Time. Especially with his Michael Jackson squeal. Downplayed in later seasons, as not at all present in his modern "Mr. Gold" persona.
Upon hearing a historian's theory that Adolf Hitler was gay, The Tina Fey/Jimmy Fallon incarnation of Saturday Night Live's Weekend Update introduced a recurring character Gay Hitler, played by Chris Kattan.
Ratallack of The Shadow Line. He's an extremely campGayngster who's ruthless enough that he'll order the death of his own boyfriend to improve his position.
Jim Moriarty from Sherlock. He's dressed to the nines and can be outright flaming, although he says he's only playing gay.
Kivas Fajo from the Star Trek: The Next Generation episode "The Most Toys". He'd be delighted to watch Data go around naked.
Supernatural: Crowley spouts Double Entendre like its going out of style, is fond of calling people "darling", "sweetie", "kitten", "handsome", etc. and is smartly dressed and cultured. He's also a Depraved Bisexual who will kiss men to make deals with them and in season 11 he possesses a women who has sex with her husband in a foursome with another couple before killing them all.
Super Sentai occasionally plays the trope very straight:
Highness Duke Org Ura, the second Arc Villain of Hyakujuu Sentai Gaoranger has an effeminate tone to his voice, feminine mannerisms, wields a paper fan as his weapon and even has an obsession with pretty things such as jewels. Even his catchphrase and laughter are those typically associated with noblewomen.
Sorcery Priest Meemy, the second Arc Villain of Mahou Sentai Magiranger, similarly to Ura above, has his entire character be effeminate in addition to dressing in colorful robes. He also has vanity as part of his character to further accentuate.
That Mitchell and Webb Look: Leslie, a parody of Bond villains, is a Diabolical Mastermind evil genius with very effeminate mannerisms and constantly talks in an uncomfortably seductive tone of voice. A Euphemism Buster by one of his minions leaves no doubt whatsoever.
Leslie: Perhaps you'd like to join me for some... refreshment later? Minion: So you really mean anal sex?
In The BBC's 1960s adaptation of The Three Musketeers, Rochefort is shown to be an incompetent fighter (he falls on his arse from surprise when d'Artagnan challenges him into a duel) and he's seen crying after a minor injury. He's also wearing very light-coloured clothing and spends more time adjusting his shoes and swishing his cloak than doing any actual menacing.
Captain John Hart is the ultimate aversion of this trope. Violent, evil, snarky, and can beat the crap out of anyone you care to name.
His good counterpart, The Hero Captain Jack Harkness, was once described as a homophobic TV viewer's nightmare. An arse-kicking, quipping queer. Bonus, his actor is gay, despite the character being 'omnisexual'.
