Multipurpose Monocultured Crop

It's common for World Building writers to Hand Wave the agricultural practices of their fictional planet, Lost World or fantasy culture. When mentioned at all, often this topic will be minimized by letting virtually all of an invented society's needs be met by just one or two domestic crops, or a single kind of livestock. If a plant's roots can be eaten half a dozen ways, its stems burned for fuel, its leaves converted into textiles and its sap brewed into alcohol, it's this trope. Likewise, if the dominant livestock is an easily-reared Explosive Breeder that (conveniently) supplies all the dietary needs of a population on its own.

The agricultural equivalent of Green Rocks. If this particular crop/livestock's production is the foundation for an entire culture, it can help define a Planet of Hats or One Product Planet. May be an indication of current or Lost Organic Technology within the setting. Soylent Soy may be an example, if derived from a single crop species rather than blending two or more.

Examples of Multipurpose Monocultured Crop include:

Anime and Manga

Robotech has the Invid Flower of Life. Scientific discoveries derived from this plant triggered the protoculture wars, as the Robotech Masters seek to control its secrets, the Invid go on a genocidal Roaring Rampage Of Revenge in response, and Earth is caught in the middle. Among the products produced from it:

Chemicals used in genetic engineering, allowing the creation of the Robotech Masters' Henchmen Race, the Zentraedi.
A drug that gives virtual immortality to the Robotech Masters.
A catalyst critical to operation of the Robotech Masters' FTL drive.

Literature

In the Humanx Commonwealth series, Home Trees of Midworld provide food, shelter, and an organic security-system. Pika-pina, from Tran-ky-ky, can be made into sailcloth, paper or rope, its nutrient-rich nodules are edible raw or cooked, and its leaves can be eaten plain, ground into flour, squeezed for juice or dried out as bedding.
In The Light Fantastic, Cohen the Barbarian spends time with a clan of horse nomads, who use horses for transport, meat, horsehair robes, leather, milk, and a thin beer best not inquired about.
"Swist" from the children's story Weslandia:

Grows super-fast
The fruit is delicious, and the rinds can be dried into cups
Excellent tubers
Leaves make a good spice
Inner fibers can be spun into clothes
Oil from the seeds acts as suntan lotion and bug repellant
The crop attracts a whole ecosystem of pleasing animals

In the Vorkosigan Saga, Esteban Borges's artificially designed and created "Butter Bugs" are meant to be this. They are large bugs that live in colonies with a Queen and reproduce quickly, yet their breeding is human-controlled so they can't overrun the environment. In their stomachs they secrete 'Bug Butter', which is tasteless, sort of the consistency of tofu, and can supply all your dietary needs: you can practically live of it alone. Their excrement is also excellent fertilizer, and they can be kept at low cost since they can eat just about anything that's organic, including bark, branches and grass. Their marketing didn't exactly take off at first, as people were turned off by their ugly appearance and thought it was pretty disgusting to eat something that was regurgitated by one, until Ekaterin redesigned them to be "Beautiful Butter Bugs". Now it seems they're going to be pretty profitable.
In The Lorax, the Once-ler uses the tufts from the Lorax's truffula trees to make all-purpose consumer products known as thneeds. Subverted in that the truffula trees aren't being cultivated, just harvested from the wild until there's none left.

It's a shirt, it's a sock, it's a glove, it's a hat
And it has other uses, far beyond that

Live-Action TV

Radishes in Fraggle Rock. For Fraggles it's their main food source. Doozers use it as building material (which is why Fraggles find it delicious, although they don't know about it). Gorgs, who grow it in the first place, use it for anti-vanishing cream, which keeps them from fading away to nothing.

Music

"The Wompom", a song by Flanders and Swann, about the world's most miraculous, all-purpose plant.

Newspaper Comics

The shmoo, from Li'l Abner, provides meat (several flavors), milk, eggs, butter, leather, wood-substitute, buttons and toothpicks. The milk, eggs and butter come already bottled/packaged.

Tabletop Games

The 1st Edition Dungeon Master's Guide for Dungeons & Dragons recommended that DMs incorporate some made-up variety of vegetation or prey into their campaign worlds, that can generate lots of easy food and thus make the abundance of big predatory monsters a bit less implausible.
Warhammer 40,000: Many inhabitants of the Imperium of Man subsist on grox, an aggressive breed of reptile which has replaced cattle.
In the Talislanta game, parts of the viridia plant can be used for everything from flour to fabric to lumber to oil to naturally-grown canoes. Justified by A Wizard Did It.

Video Games

Dwarf Fortress has no universal plants, but a few crops are more versatile than "eat or brew". Quarry bush leaves can be cooked as is or ground into flour, while its seeds ("Rock nuts") can be pressed for cake (also cookable) and oil (which can be used in cooking or to make soap); Pig tail and Rope reed are not edible, but both can be brewed into alcohol or spun into thread for cloth and ropes.
- Animals can be shorn (again, thread gives both cloth and ropes), milked (which allows to make cheese) and butchered for edible parts (meat, fat, etc), leather (uses range from bags and wineskins to armor, and it's the only common material good for quivers and backpacks) and bones (can be made into crossbow bolts and some armor pieces) plus hooves and horns if appropriate.

Real Life

Soybeans are a Real Life example, being the source of numerous processed foods and food additives, as well as oils useful in biodiesel, soap, cosmetics, inks, solvents, crayons, and clothing.
Maize (corn) is grown for food, alcohol, starches, biofuel, corncob pipes, mazes, autumn decorations and herbal corn-silk remedies. In the 19th century, corncobs were also commonly used as toilet paper, and corn husks, as packing material or insulation.
In Colonial America, farmers claimed they used "every part of the pig but the squeal".
- In another part of the world, that is what the Chinese are doing right now: For every single part of a pig there is at least one Chinese dish out there using it.
The miracle tree (Moringa oleifera) is an awesome example of this. Originally from Southeast Asia, they are now used in many subtropical parts of the world to help combat malnutrition. Immature green pods of the tree are said to have a kind of green bean with a hint of asparagus taste, its seeds are roasted like peas or nuts, the flowers taste like mushrooms, and the roots can be shaved into a horseradish-like condiment.
- According to this article: Moringas are among the world’s most nutritious plants. Their leaves can be eaten raw, cooked, or ground into baby formula. They contain four times the calcium of milk, three times the potassium of bananas, four times the Vitamin A of carrots, seven times the Vitamin C of oranges, and about half again the protein of soybeans. The seeds can be pressed for an unsaturated fat like olive oil or crushed into a powder that purifies water(!): its electrolytes attract impurities and precipitate them out of the fluid. Best of all, Moringas are fast-growing and extremely drought-tolerant.
Hemp can be used for food (the seeds), medicine (against aczema and inflammation), as rope, for fabric for clothing, sacks and sails, as building material, as jewelry, it can be made into paper and plastic, and it can be used for fuel, weed control and water purification. And yes, it has that other use too.^{[please verify]}
- Then again, it's rare to encounter a culture that actually uses it for all these uses and has no other crops. In that light only corn can really count.
After the work of George Washington Carver, peanuts come close.