Lala the demon who takes the form of a teenage girl from the "Manga/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.
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 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.
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.
At one point, she even manages to be a drama queen while writing a letter.
Rainbow Dash and Twilight Sparkle can also be big Drama Queens. Once, both truly believed all her dreams would be crushed and Princess Celestia (often mistaken to be a tyrannical dictator) would have them thrown in a dungeon,or banished,or thrown in a dungeon in the place they were banished to, simply for the most little of failure.
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.