Many thanks to Ryusui for the writeup.

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 matter (well, the servers it's stored on are, anyway).

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.

Examples:

Anime & Manga

• In 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.

Comics

• Transmetropolitan has these and they seem to also come with an AI.

Film

• Tesla's attempt to create a teleporter in The Prestige 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 to the point that Angier, who kills his duplicates as part of his magic act, isn't entirely sure if he's not a duplicate himself.

Literature

• Robert Heinlein's Future History timeline included a "Universal Pantograph" which could duplicate objects. It's mentioned in Time Enough For Love.
• In the Vorkosigan Saga there are replicators for organic material, but it's implied that traditional manufacturing is easier for metals.
• William Gibson's All Tomorrow's Parties has the Nanofax machine, which transmits copies of anything.
• Diamond Age by Neal Stephenson pretty much revolves around this trope.

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).
• In the 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.
• The more advanced races of the Stargate verse have them, but they don't show up very often.
• Farscape had an episode where a villain used a wrist mounted version to "twin" people.

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.

Tabletop Games

• Shadowrun features these, what with it being a melting pot of cyberpunk tropes and all.

Web Comics

• The fabber in Schlock Mercenary is an odd case of a Matter Replicator that uses mechanical labor.