Merging Machine

Basically it's a device that fuses multiple objects together, kind of like Fusion Dance. Works by either shooting a beam or placing the objects into a machine. May also work in reverse. Sometimes, the effect is unintentional and probably not the main purpose of the device; Teleporters and Transporters are particularly prone to becoming Merging Machines when something goes wrong, especially in cases such as Tele Frag.

May be involved in Item Crafting.

Examples of Merging Machine include:

Comic Books

There was a strip in the 1970s British Comic Whizzer and Chips called "Minnie's Mixer", which played this for laughs. The eponymous device looked like an electric food mixer, but when pointed at two objects in close proximity could fuse them together. Most often used to mix people or pets with objects. Fortunately the process was reversible.
A case where the "merging machine" is a person: In the thirteenth issue of Grant Morrison's Animal Man series, the B'wana Beast was infected with Anthrax and it drove him a bit crazy, to the point he was using his powers to merge random animals and turning the resulting chimera into killing machines.

Film

The Fly is arguably based around an accidental version. Many parodies and homages tend to fall into this trope by having multiple "mixings" take place.

Live Action TV

Star Trek Voyager episode "Tuvix". A transporter accident fuses Tuvok and Neelix together, forming the title character.
Mystery Science Theater 3000: In the Manos: The Hands of Fate episode, Joel's invention exchange is the Cartooner, a device that takes two newspaper comicstrips and combines them into something funnier than the source material. "Ziggy had Garfield neutered?!"
Inverted and then played straight in one episode of Star Trek the Original Series, where a transporter malfunction splits Captain Kirk into two people, one with all his more aggressive traits and the other with his more passive traits. Eventually the crew figures out what caused the malfunction and successfully uses the transporter to reunify him.

Toys

Bionicle: the Spear of Fusion, which can also be used in reverse.

Video Games

Jakyou Manors/The Velvet Room/Demon Fusion Program-enhanced tech in most of the Shin Megami Tensei games, including the Persona spinoff series, function this way for combining demons, personae, swords, spell/tarot cards, and any number of other compatible things.
- There have been cases in which accepted parts for fusions have included humans (twi ce) and a dog. Most of the time, they remember their pasts. On the other hand, aggression level is raised and there is the question of getting a severe case of violent madness and eventual breakdown. Evil Is Not a Toy, kiddies!
In Tymora's Luck tinker gnomes and two gods made a "fusion chamber".

Web Comics

Homestuck's punch-card alchemy process lets you convert objects into punch-card codes and back, and by merging the codes, you can create merged objects.

Western Animation

The Ace Ventura animated series had an episode based around a scientist whose teleporter combined him with a fly. Later in the episode Ace is combined with Spike.
ReBoot had an episode where a corrupted game fused Megabyte with a containment unit filled with liquid energy. It turned him into a Megatruck.