Reality-Changing Miniature

A model or miniature of a real-world object which affects the real-life counterpart when it is changed. For example, a miniature New York where you can move buildings and they'll move in the real New York. Or a globe... careful with it... if you poke it carelessly, you'll crush the entirety of China.

Sometimes it's just some kind of a magical equivalent of the real-world object. Other times, it literally is the real-world object through some space-time shenanigans.

The term for this when used for magic is sympathetic magic, which operates on the principle that "like affects like." In many works featuring this magic, the magician often needs something that his or her victim once owned (such as fingernail clippings or a lock of his or her hair) in order for the Reality-Changing Miniature to actually work. Hollywood Voodoo dolls tend to work this way.

Anime and Manga

 * Spirit of Wonder: Miss China's Ring does this with the moon (this is the version where it is the real object due to shenanigans).
 * One of Sembei's inventions in Doctor Slump is a miniature version of his house that works like this. When Akane asks him why did he create something this dangerous, he replies "This is a gag manga. Things don't have to make sense".
 * One of the Ranma ½ movies features a pair of Go players. As they play on the normal board giant stones appear and land on the giant board that surrounds them. They threaten to crush our hero, until he realizes that he can just run on top of the stones that have already fallen. Of course this means that he has now "disappeared" from the field of play, and his opponents can't find him.
 * Bleach. The Arrancar Espada named Szayelaporro Grantz has the ability to engulf opponents with parts of his body and create voodoo dolls of them filled with replicas of their internal organs. Doing things to a doll affects the original person, and if a replica organ is destroyed, so is the real organ in the victim's body.
 * One of the members of the 7 Kin in Fairy Tail has a doll that can affect the person whose hair to touching the doll, and not only does he use it to hurt his enemies he also uses it on himself to modify his physical abilities, such as turning the doll to steel to increase his durability.
 * Yoshihiro Kira, the malevolent father of the equally dangerous Big Bad of part 4 of JoJo's Bizarre Adventure, became bound to a photograph through his Stand after death. Now, courtesy Atom Heart Father, he can manipulate the area depicted in whichever photo he's bound to. Whatever he does in the photo, happens in the actual place, and he can even trap anyone who's there. He came within centimeters of killing Josuke and Jotaro.

Comic Books

 * The city of Bete Noire from Fallen Angel is believed to be this for the entire planet.

Film

 * In the original Clash of the Titans, there was a small chamber in Olympus containing several clay figurines, each one representing a real person. The gods could resculpt the model to invoke a Painful Transformation, or just smash the thing.
 * In Stardust, Lamia is able to use a voodoo doll to kill and then puppet his corpse to fight Tristan.

Literature

 * There's an old Russian sci-fi story which features an ancient Martian mirror, which apparently works this way for whatever is reflected in it. A woman pokes a distant reflection of an incoming plane, and it ends up crashing, covered with humongous scraps of human skin.
 * In Lewis Carroll's Through the Looking-Glass, Alice encounters a chessboard with living pieces that she moves around the board and react accordingly. When she leaves the Looking-Glass House, she finds herself on a chessboard corresponding to the small one she previously found.
 * Major plot point in Wolf Speaker; To make a rather long story short, Daine has to stop a rebellion by finding a model of Dunlath Valley, so that Numair and the Big Damn Heroes can come in and finish off the malcontents.
 * Also used in The Song of the Lioness, where  had a wax figure of the Queen washing away under a fountain to represent the washing away of her life. He also has wax figures of the king, Jonathan, the Provost, Alanna, and Sir Myles in a black sack to "keep them in the dark" about his plans.
 * The Glooper in Making Money reflects the financial state of Ankh-Morpork, so it's naturally very distressing to discover that the bottle representing the gold in the bank vaults is empty.
 * Another Discworld example: in Equal Rites, Esk finds Simon (who's been posessed by the Things from the Dungeon Dimensions), shaking a glass container with a model of the Disc and giggling. The feeling creeps over her that this isn't exactly a model.
 * The Discworld gods also play games on a miniature model of the Disc with real heroes represented by playing pieces. The Disc can also be influenced by it, such as during Small Gods when  decides to start a fight around the tabletop Disc, and below in the real world large (as in, small house sized) dice and large fruit bowls start crashing about as the fight above influences what happens below.
 * In Sidhe Devil by Aaron Allston, miniature models of a city are used to cast spells that effect the real city.
 * This is the principal system of magic that appears in The Kingkiller Chronicle, though actual representative models of people and objects aren't always necessary.
 * In The Hounds of the Morrigan, the Morrigan sisters have a magical tabletop they can use to manipulate the titular hounds and chase the two protagonists. Near the very end,
 * The Chronicles of the Kencyrath short story "Bones" features one of these.
 * Thaumaturgy in The Dresden Files is defined as "make something happen on a small scale and give it the power to work on a larger scale." It's how his tracking spell works and how he once defeated a werewolf, among other feats.
 * And more specifically (and literally), Dresden's model of Chicago.

Live Action TV

 * Star Trek: The Original Series
 * "Requiem For Methuselah". Flint reduces the Enterprise to a tiny model, which puts the crew into suspended animation.
 * A Hollywood Voodoo doll version in "Catspaw". Sylvia holds a tiny model of the Enterprise over a flame, causing the temperature of the real Enterprise to rise. Korob later encases the model in crystal, which puts a force field around the real ship.

Newspaper Comics

 * There's a Pearls Before Swine strip where Pig pokes at Atlas' globe while finding himself on it, and pokes himself in the eye.

Video Games

 * The Interactive Fiction game For A Change has you come across a miniature version of the gameworld near the end. There's a flood, and you have to tip the model to spill out the water.
 * In the famous scene in Warcraft III, Archimonde shapes the dust near Dalaran into a replica of the city, then swipes his hand through the dust-model. The result is...spectacular.
 * A central dynamic in Soul Nomad and The World Eaters, where you acquire manikins of people that you use to summon their real selves into battle. A humorous scene involves Danette playing with manikin and accidently breaking its neck, which causes  to suffer some serious physical distress. Gig points out that this sort of thing shouldn't be possible.

Web Comics

 * In Amazing Super Powers (see also Alt Text and the hidden comic), Magic Map And The Magic Board Game.
 * In Chirault, the magician's guild accidentally creates a model of the world with these properties. They get scared of the model's potential for destruction and try to find some way to unmake it. Naturally, it gets stolen.

Web Original

 * This was apparently once very popular in the SCP Foundation, but has since found its way into the list of overdone cliches.

Western Animation

 * An episode of Futurama ends with the Planet Express crew in possession of a box which contains their own universe. Fry proceeds to sit on the box, making the picture become stretched out and flattened.
 * They also shook the box, which caused an earthquake.