In the Doldrums

This place is barren, and it takes steps to keep it that way.

The Doldrums is a place with the distinguishing characteristic of being boring. But this isn't your standard, run-of-the-mill boring. This is advanced boring. Here is a place that defies the normal properties of space to create a barren wasteland. Its properties may include lack of purpose, loss of memory, time dilation, space dilation, Lack of living things, and Involuntary Fading Disorder.

A variant of The Doldrums is an infinite featureless plane, often white.

Overlaps a bit with Mordor, but the key feature is the bareness, not the evilness.

Examples of In the Doldrums include:

Anime and Manga

The "Room of Spirit and Time" from Dragonball Z ("Hyperbolic Time Chamber" in the dub).

Comic Books

In the DCU, the Phantom Zone associated with the Superman franchise.

Film

In Pirates of the Caribbean, Davey Jones' Locker is a barren wasteland (for a while, anyways). Nothing but perfectly flat, white desert in every direction.

Folklore and Mythology

Sheol, in early Jewish myth, and Hades in Greek myth, were both places like this, neither good nor bad; Just gray.

Literature

Trope Namer is The Phantom Tollbooth. It's home to the Anthropomorphic Personification of boredom, and you get there by not thinking.
In the Stephen King novella The Langoliers, the characters are stuck in between seconds. The resulting dead world acts in this manner, but it is fated to be eaten by Eldritch Abominations.
The interior of the house in House of Leaves.
The Crapsack World of The Road might qualify.
The Muddletop Moors in Alan Dean Foster's Spellsinger novel The Day of the Dissonance. It's overcast all the time, food is tasteless and anyone traveling through it gets so bored and depressed that they just lie down and die. It turns out that the depression is caused by the telepathic broadcasts of the intelligent giant fungi who live there. But of course, Jon Tom provided some magical entertainment to the fungi and passed through the moors safely.
Xanth gives us the Neverglades. An infinite expanse of featureless marsh that traps people within it for all eternity unless you can overcome the spell in some way.

Live-Action TV

The titular setting of the Doctor Who serial Warrior's Gate. A subversion of sorts as doing nothing is the only way to get out.
On Star Trek: Voyager, the Q continuum was described this way by a Q who had become so bored with his omniscience that he wished to commit suicide.
One episode of The Twilight Zone has a man who only wants to read be the sole survivor of every one else on earth being killed off, finally has all the time to read in the world he breaks his glasses

Tabletop Games

In Planescape, the properties of the Grey Wastes of Hades replace all emotions with hopelessness and gloom, and cause colors fade to gray.
- The same is basically true of Dollurh in Eberron, except while only some evil people wind up in Hades, everybody winds up in Dollurh.

Video Games

The Guardian's realm looks like this in The Longest Journey. It turns out to be a Fisher Kingdom—in the sequel, the replacement for the first game's ailing Guardian adds plant life and a proper sky.
The rakatan prison in Knights of the Old Republic is a big blank whiteness with a single prisoner being the only remarkable feature. Talking to him reveals that there were others as well who got trapped by accident and eventually ran off into the endless void.

Web Comics

Richard of Looking for Group gets locked in one called "the Infinite Plane of Suck."

Western Animation

One episode of SpongeBob SquarePants ended with Squidward in an endless expanse of white emptiness, until he mentioned he was, at last, alone. Cue voices saying "alone" and the word itself appearing in different colors and sizes.
There's an episode of the Care Bears like this, called "Drab City," where the titular bears find a town where everything is depressing and colorless, and all the people are apathetic. As they travel through the town, they begin to turn gray and depressed as well.
A cutaway in an early Family Guy episode showed the Griffins on holiday in Limbo. They were all just hanging in a featureless void, commenting on how it was neither good or bad.