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.
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Pictured above: Eternity, having been summoned by Hercules during the Chaos War (long story)
"Yes, there ARE rules. And you BROKE them! How dare you! HOW DARE YOU!
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 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, villain-esque way possible...
(as thousands of his worker drones come together to form a giant holographic version of his head)
YOU DARE CHALLENGE MEGAMIND?
The Nightmare Before Christmas has an (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.
In Yellow Submarine, the head Blue Meanie asks Who Dares bring music back into Pepperland. The Dragon, Max, first answers, "Rimski Korsikov?"; this gets him blasted and stomped. He next suggests "Guy Lombardo?"
In the Power Puff Girls movie, Mojo states "You dare challenge me!?". He actually manages to make it sound intimidating.
The third The Lord of the Rings movie has the King of the Dead say this when Aragorn, Legolas, and Gimli first enter his chamber.
Dead King: Who enters my domain? Aragorn: One who would have your allegiance. Dead King: The Dead do not suffer the Living to pass. Aragorn: You will suffer me! seeing as he (Aragorn) is the direct descendant and heir of the guy who made them into ghosts and all
Man-At-Arms: You dare threaten her (the Sorceress) life?!?
Skeletor: I DARE ANYTHING! I am SKELETOR!
The Russian film "Two arrows - a stone age detective story" ends with a rather poignant "who dares?!" when the clan reader realizes his political assassination tactics have caught up with him.
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:
Harry: Yes, I dare.
The other wizard named Harry is even more impudent and his enemies on occasion even more narmy. Nicodemus, the White King, the Erlking, the Winter Lady Maeve, the Black Court Wizard Mavra and others have found that there are very few lines that Harry wont cross.
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.
There is an Achievement in Xenoblade called "Who Dares Defy Me?". You get it for using Melia's Arts 100 times.
When a mimic of Spider-Man knocks out security at the Science Expo:
Dr. Octavius: Who dares? Face me coward! Face a worthy foe!
"Who dares disturb my sleep?" —Diablosnote A bunch of teenagers armed with magical monsters, that's who.
The pit fiend starts saying it too, before seeing it's Qarr who summoned him.
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 question my...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.
Circe (After taking two tables to the face): Insolent trickster! You dare to strike—! (*chair*) You dare to stri—! (*another table*) You dare to strike—! (*tablecloth*) QUIT IT! (stares) Oh no. (*piano*)
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.