Bring It Back Alive

A secondary goal of a Great White Hunter or the primary goal of an overly curious biologist. Instead of killing and mounting a unique species, their goal is to bring back one or more of them alive for display (or black market sales) in the first case, or for scientific study in the later. Generally portrayed as a negative goal in modern works, especially in the case of the Great White Hunter. However, it was once lauded as a worthy goal of any explorer and a sign of their skill that they managed to capture a dangerous beast without killing it. The Mad Scientist version of this trope has the scientist insist on using kid gloves to capture or not harm a murderous Juggernaut.

Sometimes it is a choice made after the characters accidentally subdue the animal or monster instead of kill it.

More often than not it will then escape and rampage through the city.

Compare I Want Them Alive for humans.

Anime and Manga

 * Dae in Claymore looks upon the Destroyer and laments not having the resources to capture it.

Comic Books

 * The primary antagonist of the Franco-Belgian comic book Marsupilami is named Bring M. Backalive in the original French version (or Bring de Backalive in the comic), and as expected, attempts to capture a live specimen of the eponymous animal.

Film

 * The 1925 film version of The Lost World has this occur with a "Brontosaurus" in an accidental manner.
 * King Kong is the Trope Codifier.
 * Mighty Joe Young has this occur as a publicity stunt for a night club--the owner hires cowboys to lasso lions, and finds the title character along the way.
 * Gorgo has this occur intentionally, and the animal is put on display at a circus (to the scientists' great annoyance). Then its mother shows up...
 * The goal of the exploration group in the 1948 film Unknown Island.
 * The villains in Mothra kidnap the twin fairies out of greed--getting the titular Goddess angry. Later, another entrepreneur tries to do this with Mothra's egg AND the fairies. Then Godzilla shows up too--hungry for Mothra Egg.
 * The goal of the villains in The Lost World: Jurassic Park.
 * The film Aliens has one greedy company guy who wants to bring back a live xenomorph for study, versus the people who just want to kill it before it kills them. In later films, other representatives of the company express interest in capturing a live specimens...one way or another.
 * It goes so far that in the fourth film, the military brings the last known xenomorph queen Back From the Dead and hijacks a corporate passenger ship to provide implantation specimens in order to create their own pet xenos, two hundred years after said queen is killed by a Taking You with Me Heroic Sacrifice. Unfortunately for them, the xenos have no intention of being bootlickers and are too smart to not figure out a way to escape. Fortunately for everyone else, resurrecting the queen brought back Ripley as well...

Literature

 * Willard Price's Adventure series (Gorilla Adventure, Elephant Adventure. etc.). Hal and Roger Hunt traveled around the world capturing exotic and dangerous animals for their father's wildlife collection.

Live Action TV

 * Primeval seems to have 'take it alive' as the secondary aim of dealing with incursions, if for some reason the primary aim (Return creature to time period) falls through. Of course, if they can't do that they kill it rather than let it run rampant in the modern era. Sometimes wind up being the target of Lester's Deadpan Snark "...And what am I meant to do with a mammoth?"
 * The entire point of the series Bring Em Back Alive.
 * Prehistoric Park is this trope in effect.
 * Doctor Who: The Doctor and U.N.I.T. attempt to capture one of the eponymous dinosaurs alive in Invasion of the Dinosaurs so the Doctor can examine it and work it where they are coming from.

Tabletop RPG

 * Classic Traveller
 * In 76 Patrons, one patron wanted the PCs to capture a mating pair of Rowan's Beasts on the planet Feor.
 * Adventure 10: Safari Ship is about an expedition to capture a beautiful animal on an unexplored planet.
 * GURPS Bestiary had two pages of rules on live capture of animals.

Western Animation

 * Star Wars: The Clone Wars had this done with a Kaiju, The Zillo Beast. It ends as well as you might expect when they bring it back to Coruscant (a planet-wide city and capital of the galactic republic) of all places.

Real Life

 * Literally Truth in Television for the young David Attenborough, whose early Zoo Quest programmes were about trapping animals in exotic locations so they could be brought back to London Zoo.
 * Real Life Great White Hunter Frank Buck made a career out of this.