The Chase

A plot centered around characters pursuing one another.

A drawn out chase which forms an underlying theme for a series is a Stern Chase.

They Have the Scent is common in short chases.

See also the subtrope Hunting the Most Dangerous Game.

Film

 * The Third Man.
 * The Fugitive.
 * Smokey and The Bandit.
 * Race for The Yankee Zephyr (1981)
 * The movie The Chase. Which makes it Exactly What It Says On the Tin.
 * Apocalypto
 * The Warriors (Stern Chase example)

Literature

 * Honored Enemy of The Riftwar Cycle in which soldiers on the opposing sides of a war band together to escape the dark elves chasing after them to kill them for a variety of reasons.
 * In Robert E Howard's Conan the Barbarian story "Black Colossus", after his defeat, Natohk abducts Yasmela. Conan chases after them.
 * In "The Gods of the North", an obviously magical woman lures Conan into a chase that brings him to her giant brothers. When he kills them, he chases her again -- this time, she is seriously frightened.
 * In Poul Anderson's A Midsummer Tempest, chasing the escaped Rupert is half the book.
 * The Time Scout series is full of these, starting with the second book. Mostly they involve Skeeter Jackson.

Live-Action TV

 * The William Hartnell Doctor Who episode "The Chase," in which the Daleks first develop time travel and chase him and his companions all through time and space.

Newspaper Comics

 * Dick Tracy had this as a major element in his stories as the police detective relentlessly chases a particular villain who gets more and more desperate as he realizes to his terror that this cop will not stop.

Web Comics

 * Snuggleninja is always chasing the butterfly.
 * In Sinfest, after Death realizes the zombie's a fugitive, the chase is on.
 * Also, annually, Death has to chase down the year, who always tries to make a break for it.

Western Animation

 * Pepe Le Pew and his kitty.
 * Roadrunner & Wile E. Coyote.
 * Bugs Bunny and Elmer Fudd/ Yosemite Sam/ various unnamed characters, Sylvester and Tweety Bird/ Speedy Gonzales/ various unnamed characters, Tom and Jerry, Dick Dastardly and Yankee Doodle Pigeon, Gargamel and the Smurfs, etc., etc., etc., etc., we get it, cartoons involve chasing.
 * The entire plot of the Danny Phantom episode "Reality Trip". The Guys in White constantly pursue Danny and friends after Danny accidentally exposed his half ghost power to the public.
 * This troper can't recollect a full episode devoted to this, but is willing to bet that The Simpsons have done it.
 * The episode "The Chase" of Avatar: The Last Airbender stands out among numerous episodes dealing with the Fire Nation's pursuit of the heroes.