Fiction
The term grey goo is often used in a futuristic or science fiction context, as the required technologies do not yet exist. In the worst postulated scenarios (requiring large, space-capable machines), matter beyond Earth would also be turned into goo (with goo meaning a large mass of replicating nanomachines lacking large-scale structure, which may or may not actually appear goo-like). The disaster is posited to result from a deliberate doomsday device, or from an accidental mutation in a self-replicating nanomachine used only for other purposes, but designed to operate in a natural environment.
In the manga Battle Angel Alita the planet Mercury has been been classified as a no-go zone after a scientist turned the planet into an invincible ball of grey goo that engulfs anything that goes near it, like space probes and other machines.
Notable examples of such a work can be found in the novel Blood Music by Greg Bear (1985), the 2002 Michael Crichton novel Prey and Wil McCarthy's novel Bloom. The remake of The Day the Earth Stood Still features a grey goo nanoattack on human civilization.
In the video game Deus Ex: Invisible War, a limited form of "grey goo" has been weaponized to create so-called Nanite Detonators, a potent weapon which uses self-replicating nanites to consume an entire city, yet which is not capable of running amok across the Earth's surface.
Broken Angels, the third novel in sci-fi author Richard Morgan's Altered Carbon trilogy, features an encounter with an evolving, self-replicating colony of nano-machines.
In the Thursday Next novel Lost in a Good Book by English author Jasper Fforde, the main character is warned of an impending apocalypse where all life on Earth had been converted into strawberry-flavoured Dream Topping, in a botched attempt to end world hunger. This was described as an example of a "pink goo" scenario.
In the novel Aristoi by author Walter Jon Williams, the original Earth was destroyed by "Mataglap Nano", a grey goo disaster which originated in Indonesia (thus the name, which means berserk in Indonesian).
"Benderama," a sixth-season episode of the animated series Futurama, uses grey goo as a plot device. Bender uses a replicating device to create two smaller copies of himself, each of which does the same. The process continues until the new Benders reach the atomic scale and begin synthesizing ethanol to use as fuel, causing everyone on Earth to become severely intoxicated.
Jeff Carlson wrote a series of novels (Plague Year, Plague War, and Plague Zone), which took place in a world where microscopic self-replicating nanotechnology robots escape from a lab in California and kill every living organism living below 10,000 feet. The world's survivors live atop mountains in the Alps, Rockies, Andes, Himalayas, etc and make short trips into the plague zone for vital supplies.
In the YA novel Specials by Scott Westerfeld, Shay releases a canister of nanobots that reduces an entire entire armoury and it's contents to silver goo. The reason Scott Westerfeld used silver over grey was merely for visual effect.
Computing
Denial-of-service attacks in the virtual world Second Life which work by continually replicating objects until the server crashes are referred to as grey goo attacks. This reference refers to the self-replicating aspects of grey goo. It is one example of the widespread convention of drawing analogies between certain Second Life concepts and the theories of radical nanotechnology.