Standard villain or otherwise ominous being Stock Phrases. Said in a booming deep voice, the villain rhetorically asks Who Dares? whatever action the hero has done; be it defy them, attack them, talk to them, look at them, etc. Expect them to start referring to themselves in the third person, and giving themselves important sounding adjectives.
Possibly has something to do with the odd word-order (you don't say "How do you dare?") making the phrase sound like Antiquated Linguistics, always the domain of the overimportant egotist.
Proper heroic form, incidentally, is to stand tall and reply "I dare!"
"How dare you!" is a common variant used by heroes and villains alike, the former usually in response to the villain Kicking The Dog.
Any villain using this will usually give a "This Cannot Be!" variant upon defeat.
Examples:
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Comics
Of courseDoctor Doom plays this every chance he gets.
From Legion of 3 Worlds #2, when Mordru is angry at Superbratman-Prime's appearance:
Mordru: Who dares disturb Mordru? Superboy-Prime: Who dares question my dare? Mordru: What?
In Sandman, Desire starts in on Dream for banishing Nada to hell, earning a cold "You...dare..." from Dream. Desire's totally unimpressed.
In one of the Avengers Heroic Age comics where the Avengers are battling Apocalypse, Iron Man traps him in a forcefield. Cue the following exchange
In Labyrinth, when Sarah tries to enter the Goblin City, the gate slams in her face...and each wing of the gate has half of a golem, which grabs a huge axe and starts swinging it back and forth while repeatedly booming "WHOOOOO GOES?!...WHOOOOO GOES?!"
In Yellow Submarine, the head Blue Meanie asks Who Dares? bring music back into Pepperland. The Dragon, Max, first answers, "Rachmaninoff?"; this gets him blasted and stomped. He next suggests "Guy Lombardo?"
"Yes, there ARE rules. And you BROKE them! How dare you! HOW DARE YOU!
The Nightmare Before Christmas has a(n anti)heroic example. During the final confrontation with Oogie, Jack bellows "How DARE you treat my friends so shamefully!?" in the most righteously indignant way possible.
King Osric: What daring! What outrageousness! What insolence! What arrogance! ... I salute you.
In more a homage to this trope than anything, at the start of the climax of Megamind, as the titular character finally realises it's worth risking everything to correct his mistakes, the former Supervillain announces his presence in the most dramatic, villan-esq way possible...
[as thousands of his worker drones come together to form a giant holographic version of his head]
Undead King Joseph attempts to intimidate the player like this in Age of Wonders: Shadow Magic. Then he remembers that he was only a minor villain who died in all endings of the first game, and immediately decides it would be much smarter to get on the player's good side.
Literature
Voldemort, twice, in the last Harry Potter novel, when Harry calls him by his real name ("Riddle") during the Final Battle. It's always met with the same derisive response:
Lucy, now fully undead, calls this out in some versions of Dracula after the heroes stop her just as she is about to feed on a child.
Played fairly straight in one Star Wars novel, where Mara Jade strolls into the lair of the Big Bad to save the main character in a Big Damn Heroes moment:
In the Hand of Thrawn duology, the booming automated voice whenever someone enters Thrawn's personal cloning chamber:
"Who dares disturb the sleep of the Syndic Mitth'raw'nuruodo?!"
Live Action TV
Every Go'auld in StargateSG-1 play this straight; naturally O'Neil mocks them for it every chance he gets. Eventually, by the episode Zero Hour it becomes:
Ba'al: You dare mock me?
O'Neill: Ba'al, come on! You should know. Of course I dare mock you.
ANGELUS: Defy who? A big scary voice? Whoa! Hey, I got one of those, too. You wanna hear it? (cups his hands over his mouth) You can kiss my vampire ass!
Music
In Devin Townsend's concept album Ziltoid the Omniscient, the Sixth Dimensional Planet Smasher makes his entrance growling "Who dares awaken the Planet Smasher?"
The Nox Arcana song "Hall Of The Witch Queen" opens with dramatic thunder and a shout of "WHO DARES INTRUDE UPON MY DARK DOMAIN?!"
Web Comics
A Penny Arcade strip had a book containing the lines:
A voice was heard to say, "Who dares disturb the Crypt Of The Immortal Space Bitches?" "I am Grimm Shado," said Grimm Shado, his triple wand claws extending. "And I am here to take it to the limit."
In Gunnerkrigg Court Ysengrin demands this of Renardine after seeing him in his wolf form. After Renardine's response is to mock Ysengrin's appearance, then his superpowers, the Alt Text mentions "The answer is yes".
A Robot Chicken sketch had George W. Bush discover he was a Jedi. He then used his lightsaber to vandalize the Lincoln Memorial only for it to rise from the ground and reveal a hibernating Abe Lincoln underneath...
Lincoln: Who dares disturb my slumber? Bush: Well who dares defy the...daring...of his dare?...jerk?
Aku of Samurai Jack is particularly good at this, playing it utterly straight in his first confrontation with Jack...only to subvert the trope much later on when he's visited by a group of gangsters that don't merit the full Who Dares? speech.
In Legacy, series finale of Superman: The Animated Series, Superman and Darkseid have finally come to blows in the climax of the series. As Darkseid mercilessly devestates Superman with the Omega Beam, Superman manages to get close enough to finally lay hands on his foe. However, unlike many of the entries on this page, Darkseid really is that powerful, and regards Superman's blows more with confusion than anything before he grabs Supermans fist, crushing his hand as Darkseid drags the Man of Steel to his knees.
Circe: Insolent trickster! You dare to strike...*smacked with a table* You dare to strike... *smacked with a chair* Youdaretostrike... *covered in a tablecloth* QUIT IT! Oh, no... *pianown'd*
Not villain-ish, but a few episodes of The Backyardigans invoke this trope. A good example, in High Tea:
Grumpy Emperor Austin: WHO DARES RING MY DOORBELL?! Tasha: It's me, Tasha. Tyrone: And me, Tyrone. Uniqua: And Uniqua. Pablo: And Pablo.
In the G3 movie Twinkle Wish Adventure, when the ponies approach the dragon's cave, they are greeted with a booming, "Who dares disturb the dragon?" However, when Pinkie Pie states their names and business, the voice instantly changes to a friendly tone and welcomes them in.