Every Proper Lady Should Curtsy

A typical greeting done by a female, it has long been considered to be a gesture of respect, though it is less common nowadays. For all variants of the curtsy the female bends her knees, sometimes sweeping one foot behind the other, and holding her skirt in both hands.

Furthermore, most servants would be expected to curtsy to their masters, mistresses or to someone of a higher social standing, like royalty. Female dancers may also curtsy at the end of a performance, or before engaging in a dance with another person. Note that for some, like The Ditz or the Cute Clumsy Girl, this may be a difficult thing to do. They may be used to contrast a Proper Lady who will, naturally, be an expert.

Can also be done in a mocking manner, as a sign of disrespect.

It's also a common part of those Regency-Debut to London Society type books. Specifically, the formal presentation to the queen, where the presentee has to curtsy before the queen. There's a little info about it here, after the fourth picture.

Examples of Every Proper Lady Should Curtsy include:

Anime and Manga

In episode 11 of the anime Ghost Stories a Creepy Doll named Mary does this at one point.
In Victorian Romance Emma the eponymous Emma, being a maid, frequently curtsies.
Dr. Fennel from Pokémon Black and White does so in her animated appearance, using a lab coat instead of a dress.
Early on in Bleach, when Rukia and Orihime meet for the first time, they exchange curtsies. Rukia, however, is significantly more polite than she acts otherwise (she calls Orihime "Inoue-san" in that encounter, rather than merely "Inoue") as part of the facade she assumes around Ichigo's classmates.
Relena does the mocking version in the first episode of Gundam Wing, directed at a soldier who's dragging her father away for more work immediately after he returned from a business trip.
- Much later, when Relena decides to become the Queen of the World, Dorothy makes a curtsy in front of her.
In Kyo Kara Maoh! episode 85, Yuuri who's disguised as a girl, does this.

Comic Books

The Powerpuff Girls #62 story "Brat Trap": In the standard "the day is saved" panel of pulsating hearts, Bubbles and the girls' friend Abby (created specifically for the story) exchange curtsies.
Dynomutt #1 (Nov. 1977): Not only does Dynomutt's young friend (actually a villainess) Goody Twoshoes curtsy to Blue Falcon, she lifts her skirt up high enough to provide a Panty Shot.

Fan Works

In Futari wa Pretty Cure Dragon, Ryan Lee is a male example; he even gets it right the first time! Susan Chan also does this, and as frequently as Ryan.

Film (Animated)

All Dogs Go to Heaven: Anne Marie curtsies to Charlie's friends after being introduced.
In Alice in Wonderland, the Queen of Hearts demands that Alice curtsy whenever she addresses her.

Film (Live Action)

Charlie and the Chocolate Factory: Upon meeting Willy Wonka the first thing Veruca does is curtsy.
In the movie version of Tracy Chevalier's Girl with a Pearl Earring, Griet does this often.
The cast curtain call at the end of the 1956 film The Bad Seed tops off with little Patty McCormack curtsying to us.
Done in a joking, but not mocking manner in Johnny English, when Rowan Atkinson's titular character is accidentally crowned.
Justified in The Queen since that is obviously the expected etiquette for women meeting the Sovereign of Britain. In fact, when she meets the mourners of Diana in public, the fact she encounters a whole line of Britons including women eager to curtsy to her, it's a welcome sign that she still has their respect.

Literature

Ella from Ella Enchanted is depicted as being very clumsy at the beginning stating that "curtsies often make me fall over". Her father wishes for her to become less clumsy and more ladylike and sends her to finishing school. Ella rebels against the stern teachers at the school but eventually gives in to their teachings, until she runs away. The next time her father sees her she's much more graceful and able to do a perfect curtsy.
Alice in Wonderland - Alice is constantly doing this when meeting various Queens, and one of them even tells her to cursty while she's thinking what to say. Apparently, it saves time.
In The Silver Chair, Jill just bows, as she wasn't taught how to curtsy. She learns how in the next book.
In the American Girl story "Happy Birthday, Molly!" one of Molly's friends tries to curtsy while wearing pants when she meets the English girl, and she says that she thought English girls always did that.
Done all the time in The Wheel of Time. Always.
Referenced in Tiffany Aching books. When Tiffany won't give a proper curtsy, due to her status as a witch, the Baron's son Roland gives her a dictionary with a sort of half-curtsy marked as a joke.
Done by Samantha Sweeting in Undomestic Goddess She curtsied to Trish because she thought that was what she was supposed to do as a housekeeper . Trish decided she liked it and made her keep doing it.

Live Action TV

In the Xena: Warrior Princess episode "Warrior... Princess", Xena's cover as a high-class lady is nearly blown by a bad curtsy:

Prince: She's attractive enough, but that curtsy was abominable! I thought you said her manners were impeccable?
Servant: They were!

In the I Love Lucy episode, "Lucy Meets the Queen," Lucy practices a 'perfect curtsy' so relentlessly that she ends up with a severe charley horse that threatens to compromise Ricky's 'Trained Horses' routine, and her own chance to meet the Queen.

Theatre

At the end of The King and I, after the King dies, Chulalongkorn's first act as the new King is to abolish the Pose of Supplication. He orders the men to bow to show respect, and calls on his mother, Lady Thiang, to demonstrate how "the ladies will make dip, as in Europe."
Kind of a running gag in The Sound of Music, as Georg Von Trapp's adorable daughters (particularly little Gretl) do it from time to time, especially, if you're using the film's moves, in "So Long, Farewell."

Video Games

Franziska von Karma from the Ace Attorney series regularly does this in a self-aggrandizing manner.
Zelda games take place in a fantasy version of medieval times, and curtsying wasn't really around back then. But Princess Agatha of The Legend of Zelda: Twilight Princess does when you give her one of the golden bugs.
In World of Warcraft the Alliance female characters, except the Night Elf, curtsy; it's associated with the /bow command.
Happens often in Rule of Rose. But there it's just kind of creepy.
This is Ilya's preferred form of greeting in Fate/stay night.
Until she gets used to acting like a commoner, this is how Princess Garnet from Final Fantasy IX says hi. Oooops.

Western Animation

A Pictured above: Lila does it in the Hey Arnold! episode "Helga's Masquerade" when trying to teach Helga how to be more feminine.
Penny in The Proud Family refuses to curtsy to her partner during a ballroom dancing class, "Because it signifies subservience."
Lydia Deetz curtsies at the end of the Fox Beetlejuice opening.
The Flintstones episode "The Return Of Stony Curtis": Posing as Wilma's "French maid" (in Wilma's attempt to put on airs for the visiting star Stony Curtis), Betty curtsies twice.
Sometimes in Animaniacs when the Warner Brothers bow, Dot curtsies.
On Family Guy, Lois curtsies when she meets the Pope.

Real Life

At the close of every ballet class and performance, dancers perform what is known as "reverence", or a series of curtsies: to the teacher, the audience, and the orchestra/pianist, as applicable.