Although many people consider the phrase "Chekhov's gun" to be the equivalent of foreshadowing, the statements the author made about it can be more properly interpreted as meaning "do not include any unnecessary elements in a story."
The name Chekhov's gun comes from Anton Chekhov himself, who stated that any object introduced in a story must be used later on, else it ought not to feature in the first place:
Later on, Ahasuerus suffers a bout of insomnia, and when the court's records are read to him to help him sleep, he recalls the services rendered by Mordechai in the plot against his life; Ahasuerus, however, is told that Mordechai has not received any recognition for saving his life. Just then, Haman appears, and King Ahasuerus asks Haman what should be done for the man that he wishes to honor. Thinking that the man that the king wishes to honor must be himself, Haman says that the man should be dressed in the king's royal robes and led around on the king's royal horse. To his horror, the king instructs Haman to do all that he suggested to Mordechai.
In the 2008 science fiction novelette The Last of the Funnies by Canadian cartoonist Mike Cope, the ink that is first introduced in Chapter 1 is believed by the protagonist to be ordinary India ink, but is later revealed to be a magical Rube Goldberg device.
Another example can be found in the twin pistols of the title character in Henrik Ibsen's play Hedda Gabler, which make an appearance in the first act but are not used to important effect until the last act.
An example in which Chekhov himself makes use of this principle is in Uncle Vanya, in which a pistol is introduced early on as a seemingly irrelevant prop and, towards the end of the play, becomes much more important as Uncle Vanya, in a rage, grabs it and tries to commit homicide.
A parody of Chekhov's gun is found in the "Pro Thunderball" episode of Upright Citizens Brigade on Comedy Central. The Thunderball field features a "Gun Circle," an area of the outfield featuring a loaded gun. However, use of the gun at any time is absolutely prohibited. In the episode, the Chekhov's gun principle indeed comes true when a player shoots the gun during a game.
The Winchester rifle in the eponymous pub in Shaun of the Dead is also a literal "Chekhov's rifle" in that it is introduced early in the film and is discovered to be a functional weapon later on.
The concept of a Chekhov's gun is used in a number of instances in the Harry Potter series of novels by J.K. Rowling. These include props such as Riddle's diary, Slytherin's locket and Ravenclaw's diadem, as well as a great many other objects and characters such as Sirius Black, Arabella Figg, and Scabbers the rat.
Many examples of the device exist in the television series Babylon 5. For instance, well before the Rangers were acknowledged verbally in the script, extras in the background would occasionally appear dressed in the Ranger costume. Over the course of season one, Delenn constructed what appeared to be modern art, and little more than a useful device for blocking of scenes, but at the conclusion of the season, viewers finally discovered what the sculpture was actually for. Other examples include the Triluminary, the "hole" in Sinclair's mind, Zathras, Morden, the Icarus, the fate of Babylon 4, and the alien healing device. Series creator J. Michael Straczynski was an advocate of the device and mentioned it often on Usenet.
In the game Ratchet & Clank Future: Tools of Destruction, Ratchet is given a Three & Three Quarters Centicubit Hexagonal Washer by the Plumber. The washer is forgotten about until the very end of the game, where Ratchet uses it to fix the Dimensionator and save his friends.
In the popular web series, Red vs. Blue: Reconstruction, there are multiple subtle hints that indicate that Church is the Alpha AI, most of which could be easily dispensed as either part of the humor or as merely inconsequential. For example, when the sinister Omega AI "jumps" into his body near the end of the first series, it has almost no affect on him; at the time, this appeared to merely be poking fun at Church's temper.