Matter Replicator

Captain Janeway will always get her coffee.

"Make sure the replicators provide every person with a blanket and food before nightfall."

—Captain Jean Luc Picard, Star Trek.

Matter. It's the stuff things are made of. You're made of matter. Your computer is made of matter. This very wiki is made of... well, information, to be honest. But it's stored on matter.

Matter also operates under certain rules that say that things (barring certain radioactive elements) don't spontaneously transform from one thing to another. If you've ever worried about spontaneously transforming into a giant pile of cherry ice cream while sitting at your keyboard, relax: the odds of such an event happening are vanishingly slim, as are the odds of your keyboard transforming into a nest of live pythons or the ceiling over your head turning into cheddar cheese and falling on you.

Those of us who like to sleep at night find security in those rules. Those of us who want to build things faster find them a nuisance. Turning an ore-rich mountainside into next year's model of automobile or a tree farm into enough copies of Time magazine to fill everyone's subscriptions takes a lot of time and energy; wouldn't it be better if you could just take a big pile of stuff, break it down into the very building blocks of matter and reconstruct it into all those wonderful big complex things?

Works of Speculative Fiction like to take that "if" and make it a reality. Enter the Matter Replicator, a form of Applied Phlebotinum that gleefully ignores the laws of thermodynamics as it reassembles matter to do everything from fixing a radio to fixing a nice cup of Earl Grey.

Note that the name "Matter Replicator" is itself somewhat misleading; it's rare to find one that can actually make something out of nothing (the one law of thermodynamics that usually can't be broken without breaking Willing Suspension of Disbelief as well). A Matter Replicator uses pre-existing matter to replicate something else, or perhaps even construct something entirely new. Creations made of Hard Light need not apply here. But Nanomachines often do.

Examples of Matter Replicator include:

Anime & Manga

Fullmetal Alchemist, Alchemists are basically walking matter replicators. While most Alchemists specialize in a particular kind of transformation, it's implied that with the right transmutation circle, an Alchemist can do practically anything...except, of course, resurrect the dead. Seriously, it's a bad idea to even try it.
Bokurano explores this trope quite a bit, due to the giant robots regenerating and the teleporting. Dungbeetle explains that all matter is made up of building blocks with four switches, which he can alter at will, making different things. Conservation of mass still applies, however, and Dungbeetle never creates anything out of thin air, stating that the energy difference would be too great. He uses it to teleport things instead.
Narutaru has mons with the ability to replicate anything they see. Whether this is unlimited is questioned, but it is never explored in-depth.

Comics

Transmetropolitan has these, which all seem to come with an AI. Spider's mafia-made one spends most of it's time producing drugs. For itself.

Film

The Prestige, Tesla's attempt to create a teleporter creates one of these instead; there is no explanation given for where the matter it uses to create its duplicates comes from, but in a rare event, the device is capable of copying an entire human being perfectly.
Forbidden Planet, Robbie the Robot has a replicator built in to his body, able to reproduce anything he's given a sample of. One of the crew quickly takes advantage of this and turns him into the world's fastest distillery.

Literature

Robert Heinlein's Future History timeline included a "Universal Pantograph" which could duplicate objects. It's mentioned in Time Enough for Love.
Vorkosigan Saga, there are replicators for organic material called "protein vats", but it's implied that traditional manufacturing is easier for metals.
William Gibson's All Tomorrows Parties has the Nanofax machine, which transmits copies of anything.
Wil Mc Carthy's The Queendom Of Sol series, fax machines can print copies of almost any object, as long as enough raw materials are on hand. These devices are a relatively rare example in that they can also print copies of people—potentially multiple copies, which factors into the setting's society and laws. Combined with a solar-system-wide computer network, the faxes are effectively a form of transport, medical facility, factory, and glorified refrigerator all rolled into one. They are also one of the few valuable objects in the setting's economy, as the print plate of a fax machine is one of the very few things that another fax cannot produce.
The Culture of Iain M. Banks's novels. The protagonist of Use of Weapons complains when he asks a ship Mind for some rubbish to shoot at, and is instead given a block of ice. The Mind explains that it doesn't have rubbish - just "matter that's currently in use, and matter that's available to be recycled and used for something else."
Troy Rising "fabbers", much like their Schlock Mercenary counterparts, can build just about anything you want very quickly as long as you've got the raw materials. Much like the Schlock Verse, the crushed remains of enemy ships are frequently fed in as the raw materials in question.

Live Action TV

Star Trek: The Next Generation has food replicators as a staple of shipboard life. There are also medical replicators that can produce replacement body parts and organs (including an entire replacement spine). Furthermore, Starfleet ships and stations use replication functions in their life support systems to efficiently purify the air into appropriate gas mixtures for reuse, thus forgoing the need for massive gas storage.
- In Deep Space 9 we get told about Industrial Replicators that are being sent to the Cardasians. By inference these are the industrial complexes to the cottage industry of the shipboard replicators as a small number of these is the Federation's answer to rebuilding Cardasia Prime.
- Since Star Trek replicators are use the same basic technology as transporters, there are instances of transporter accidents replicating people.
- Fan theory says that when transporters break stuff down, each wavicle is nanoscopically tagged with its position and energy in the original (in the same way that packets on the Internet are tagged with their position in the original message.) This is why Voyager finds it more energy-efficient to beam up foodstuffs from a planet (and have them cooked by Neelix) than to replicate them: information is energy, so replicators consume energy arranging matter, whereas transported matter comes with the information to arrange itself.
Twilight Zone episode "Valley of the Shadow", the inhabitants of the titular valley have advanced technology including a machine that can create any solid object based on its molecular pattern.
Stargate verse The more advanced races have them, but they don't show up very often. The final episode makes the logical point that Teleporter=(Matter Replicator + Radio), so if you have one you have the other.
Red Dwarf episode "Demons and Angels" features a matter replicator, with a caveat: all the virtues of the replicated object go into one copy, all the evils into another.
Farscape had an episode where a villain used a wrist mounted version to "twin" people.
Blake's 7: The People of Sardos have this technology, and are able to replicate anything from a tennis ball to a star cruiser using their living computer, Moloch.
Power Rangers in Space: The Astro Megaship has such a device, called the Synth-o-tron. It's mostly used for producing food and beverages, although the Rangers prefer the fare at the Surf Spot.

Tabletop Games

Shadowrun features these, what with it being a melting pot of cyberpunk tropes and all.
GURPS: Ultra-Tech They're balanced by truly massive power demands that require "cosmic" energy sources to be economical.
Cthulhu Tech makes mention of nanoforges, devices that are used both in the industrial and consumer sector, that utilize specific matter codes to construct new things.

Video Games

Homeworld, Used to justify the Ridiculously-Fast Construction seen in the games, described in surprising detail in the fluff.
Fallout: New Vegas utilizes them in the form of the Sierra Madre Vending Machines. They can turn casino chips into other things like ammo, food and medicine. These chips are made from just plain scrap metal and some form of fissionable material, if the crafting window is to be believed.
Hostile Waters has nanotechnology that acts like this as one of its themes. Creation engines were invented that could build anything from nothing, atom by atom. Attempts to regulate the technology by corrupt governments led to a planetwide socialist revolution, and 20 years later the world is a war-free post-scarcity Utopia.

Web Comics

Schlock Mercenary has most people using the fabbers (nanotech based factories). Full-scale fabbers have arrays of tools capable of building things as large as starships or as fine as bodies with blank brains. Smaller units use Nanotechnology instead of human sized robots seen in the very large fabber facilities.
- True replicators, however, were implemented via teraport gates. F'Sheri-Ganni have whole Dyson Spheres peppered with billions of these gates, with main power source buried in the respective star. So when several of these start working at full capacity...
A Miracle of Science, Mars gives most of the major nations of the Sol system "Autofactories" that can produce nearly anything from basic raw materials. Martians themselves can use the Nanomachines in their bodies to alter physical objects and most of their buildings are made of "smart matter" that can rearrange itself at will.

Western Animation

Transformers Generation 1: In "Cosmic Rust", one of the key ingredients for Perceptor's Corrostop compound (which undoes and protects against corrosion) runs out. There does not appear to be any more left. Because the Decepticons accidentally caused an outbreak of the titular disease, this is something of a problem. So Perceptor and Wheeljack have to work their butts off to get Wheeljack's Matter Duplicator to actually work so that the Autobots can produce all the Corrostop they need from a tiny remaining sample.
Ben 10 Ultimate Alien: Ma Vreedle used a giant machine in one episode to combine cloning mix and salt water in a bid to create 4 billion Vreedles that would have used the entire oceans of earth.

Real Life

The advent of 3D printing has brought this trope incredibly close to reality. There are even 3D printers that are designed to be built by other 3D printers, although specialized parts still need to be bought separately and you need to put the whole thing together by hand.
Claytronics, an emerging nanotechnology centering on tiny computerized "atoms" working together in tandem to construct larger objects.