Lala the demon who takes the form of a teenage girl from the "Devilman" anime, she will cry if she's hurt in the slightest or if she doesn't get what she wants, on one occasion she paused to do her makeup before resuming crying.
Tamaki of Ouran High School Host Club will act extremely emotional if anything sets him off enough. This includes having to lie down on a comfy bed, when being told about how the Lobelia academy works.
Team Rocket from Pokémon. Jessie is the most prominent one, but they all can be ridiculously dramatic at times. It's mostly the reason why they're so loved despite being so ineffective.
Other Pokémon anime drama queens include Harley, Ursala, Burgundy and Georgia.
The Twilight Child: Averted in one instance with Rarity, who runs out of taffeta while in the middle of designing a dress. Spike and the pony she's designing the dress for brace themselves for a freak out, and Rarity declares it... annoying. She then goes to look around her stores for spare taffeta.
Played with later on in regards to an older version of Rarity. Princess Twilight Sparkle and Rarity's daughter are talking when they hear Rarity scream in another room. Her daughter just calmly waits, before announcing that since she didn't hear a thump, she's not worried.
In Gone with the Wind, Scarlet's Aunt "Pittypat" was prone to overreaction and fainting, to the point where people even snap at her to stop fainting.
Jeeves and Wooster: Bertie Wooster, frequently. On being forced to sing at a "clean, bright entertainment":
"I have been subjected to a nervous strain unparalleled since the days of the early Martyrs. I have lost pounds in weight and permanently injured my entire system. I have gone through an ordeal, the recollection of which will make me wake up screaming in the night for months to come ..."
The In Death series: Divided in Death has young Chloe McCoy, who is this trope, due to her lover Blair Bissel's death. She gets murdered by Blair Bissel later, and he staged it to look like suicide.
Marcia Brady on The Brady Bunch is slightly less extreme than other examples, but she could wax hysterical with the best of them. Prime examples include her reaction to her missing trophies in "Her Sister's Shadow" and her anger at Alan for breaking their date in "Brace Yourself".
Diane Chambers of Cheers is often one, when she gets going.
"How could you? After all we've been through...! What we had together was real—and special—and now you've...cheapened it for—all eternity—by broadcasting to the entire Boston Metropolitan Area!—that I was...nothing but—an odelisk! In your...seraglio!"
Interestingly enough, her special appearance on Frasier briefly shows Diane seemingly invoking Rarity—before Rarity even existed! (Sans the fainting, of course....)
"OH, it's not that!—It's my WHOLE LIFE! It's RUINED!!!"
In Frasier, both Frasier and Niles often act like this. Every situation that could make them look bad to Society is a reason to act like it's the end of the world.
In the Monk episode "Mr. Monk Gets Lotto Fever," Natalie has one bout of this on the lottery set, which is done to demonstrate how much her personality has changed as a result of her becoming more and more distant from her duties to Monk.
Elliot is a self-confessed drama queen on Scrubs. There's also an episode titled "My Drama Queen" dedicated to J.D.'s new girlfriend.
Elliot: She's a drama queen, J.D.! When her husband was in a coma, it was all, like, taboo and exciting; but now that it's okay for the two of you to be together, the relationship's got no snap... it's got no crackle. J.D... It's got no pop. I know! Because I'm a drama queen, too!
The BBC Sherlock is a Man Child / Insufferable Genius combo, and so addicted to adrenaline that he puts bullets in the walls of his own flat when he's bored. After two and a half seasons of this behaviour, John has this to say:
"You are not a puzzle-solver, you never have been. You're a drama queen! Now there is a man in there about to die, "the game is on", SOLVE IT!"
The acting script for Little Shop of Horrors notes that Audrey should be played in a melodramatic way—not because she's being subversive or trying to parody the genre, but because she sincerely feels the emotions she expresses and "sees the world as her personal B-movie".
Fhjull Fork-Tongue, a greater devil in Planescape: Torment is bound by a deal with an angel to do charitable deeds. Though he can't reject any requests, he can evade volunteering aid, and then whine, guilt-trip, and passive-aggressively insult over every request he's obligated to comply with.
In Sticky Dilly Buns, the Camp Gay title character, Dillon, sometimes lurches this way, possibly manipulatively — as here. Also, the nerdy Ruby is a tightly-wound neurotic who reacts to many provocations by yelling, unintentionally increasing the drama levels.
Iku, from UC, lives and breathes drama. For her, if something can be complained about it should be complained about at the top of her lungs with waving arms for emphasis. At one point she even started complaning to the author that both she and Kelsi have the same color highlights.
The Order of the Stick: Julio Scoundrél (Good Version) AND General Tarquin (Evil Version). Both try to make their major actions as dramatic as possible, even though it sometimes screws up their plans and makes things miserable for their allies. Julio satisfies his desire to be an action hero by causing massive chaos and rushing in at the last moment to save everyone. Tarquin... kills a LOT of people with black humor snarking to look up to Darth Vader.
Bender from Futurama actually admits to being a drama queen a lot of the time. When he thought he had a backup system, he therefore thought he was never in any real danger when the cast was in trouble. But he acted all terrified anyway.
Rarity provides the Trope Image. She over-reacts so frequently and so spectacularly (even using her unicorn magic to summon her fainting couch) that the local avatar of chaos eventually makes fun of her for it. (At one point, she even manages to be a drama queen while writing a letter.)
Twilight Sparkle's sanity is not quite where it should be, and her Super OCD can easily develop into Drama Queen tendencies, especially when things start getting out of control. It's potentially contagious, too.
Rainbow Dash has Drama Queen tendencies, but normally she's too cool to give in to them. Still, she has her moments.
Princess Luna has the Fan Nickname "Drama Queen of the Night". A whole genre of Fan Fic depicts Luna trying to do ordinary, prosaic things ("Luna Uses a Microwave", "Luna Rides a Train", "Luna Visits the Dentist", "Luna Eats a Sandwich"), only to have them spiral wildly out of control thanks to her being very impetuous and self-confident, very emotionally sensitive, very difficult to educate, and about a thousandyears behindthe times.
Trixie turns out to be one in the Friends Forever comic series.
Courtney acts as one from the second half of Action on. An particularly egregious example of this behavior is when she breaks up with Duncan for the last time in "The EX-Files", dumping a bowl of spaghetti on his head and throwing an outright tantrum in the Total Drama Plane's cafeteria.
Blaineley tries to act like one; however, it comes off more as Large Ham.
Because of her fame mongering, Dakota can act as one occasionally.
This is the basic premise of the MemeHitler Rants videos from Downfall, by having Hitler fly off the handle over just about anything.