Pick a Card

One of the stock magic tricks.

At its simplest, the magician invites an audience member to "pick a card, any card" out of a deck of cards, and memorize which card it is. The card is then placed back in the deck, which is shuffled, then the magician picks out a card, displays it, and says "Is this your card?"

It's rarely done now without some extra decoration, like the card appearing to leap out of the deck of its own accord, or disappear from the deck and appear in the audience member's pocket, or the correct card number and suit being written in an envelope that was sealed before the trick started.

As with sawing a woman in half, the secret to this trick is well-known, to the point that fictional works can freely spoil how it's done. The clever part is not where it appears to be: it's not that the magician has a secret way of detecting which card the mark has selected, it's that the magician has a way (a technique called the Magician's Force) of making sure the mark picks the card he wants them to pick.

In fiction, the bare-bones version is a favorite of amateurs trying to impress somebody—and they almost always fail to get the right card at the end. The would-be magician may be shown flagrantly sneaking a look at the card before putting it back in the deck (which doesn't always prevent him from subsequently identifying the wrong card at the end anyway). Another common way for the trick to fail is for the would-be magician to be caught using a deck containing 52 copies of a single card.

Another common fictional twist is for the card to turn out to not be a playing card.

Examples of Pick a Card include:

Comics

Sir Bagby: When Sir Bagby comes to rescue the magician Snerk from a dungeon, Snerk shuffles a deck of cards and invites Sir Bagby to pick one. Sir Bagby picks a card, looks to see what it is—it's Go to jail. Miss 1 turn.
The non-serious 34th issue of Marvel Comics' What if? series proposes an alternate reality where Doctor Strange and associates were this kind of magicians instead of arcane sorcerers. The Dread Dormammu's great master plan comes down to Strange having to pick a card, any card.

Film

When Rachel first goes to the Shelter Mountain Inn in The Ring the manager does this routine with her. The first couple of times she tells him it isn't her card. The last time she tells him that it is her card just to get him to leave her alone.
The magician in Terror Train does these tricks. Being played by David Copperfield helps.
In Hugo, after Papa Georges starts teaching Hugo card tricks, Hugo is shown practicing this one by himself, using the broken automaton as a stand-in for the audience member.

Literature

Bored of the Rings:

"Insult not the White Wizard," warned Goodgulf as he drew something from his pocket, "for I have many powers. Here, pick a card. Any card."
Benelux selected one of the fifty-two sevens of hearts and tore it into confetti.

Live Action Television

In the Midsomer Murders episode "Ghosts of Christmas Past", a boy who wants to be a magician when he grows up does an actually-quite-clever version of the trick while being interviewed by the police about the murder, and his explanation of how he did it (including the fact that he arranged matters to have his own choice of card come up at the end) inspires a Eureka Moment later.
The Big Bang Theory features an episode in which Howard demonstrates such a card trick that Sheldon spends the episode trying to figure out. He's actually faking it to mess with Sheldon.
The IT Crowd:

"Pick a Card... don't show me! Put it back in the pack... is this your card?"
"No-- but damn close!"

Doctor Who: The Doctor tries and fails to do the trick at the Christmas party in "A Christmas Carol".
One episode of The Addams Family had Pugsley try it. Turns out his deck is made up only of the same card.
On Friends Joey attempted this trick, but he was laughably bad at it. He thought he was taking a glance at it so fast that no one could see. This, of course, didn't fool anyone, but they politely didn't say anything. Watch the scene..
One of GOB's illusions in Arrested Development. In one case he pulls off his shirt to show that his chest has been painted... with the name of entirely the wrong card.
There has been at least one instance of Patrick Jane pulling this trick by somehow slipping the card into the victim of the week's pocket.

Newspaper Comics

In Frank and Ernest, Frank had Ernest do this once—and found it by checking the early edition of the paper.

Web Comics

The Adventures of Dr. McNinja: The Great Flying Shooting Juan.
Kiki in Sluggy Freelance gives this a bizarre twist with her ditziness.

Western Animation

Jimmy Neutron: Sheen does this to distract the guards during the museum heist.
On Garfield and Friends, Jon tries to do the trick with Garfield, but fails. After taking out every card in the deck, Jon gives up and asks Garfield what his card was. Garfield pulls out the card with the instructions for Pinochle.
South Park episode "Super Best Friends" opens with David Blaine doing these tricks on the streets to impress the townsfolk.

Other

Penn & Teller have done several deliberately over-the-top variations, such as the one where the number and suit of the card are revealed to be printed on Teller's eyeballs. They also, as habitual lampshaders of the fraudulent nature of stage magic, have a favorite card to make their marks randomly select, the three of clubs.
- In one of their books they claimed to have contacted every pizza restaurant in the country so that you could order a "P&T Special", which was a pizza with the three of clubs made of pepperoni on it so you could pull the "was this your card switcheroo" thing on your friends. "Was this your card? No? Oh well, I'm only learning. Let's order pizza." pizza comes, friend opens it to discover their card on the pizza