World Shapes

""And that, my liege, is how we know the Earth to be banana-shaped.""

- Sir Bedevere, Monty Python and The Holy Grail

Since the most prominent force in shaping a molten proto-object large enough to later be called a planet is gravity, worlds in real life tend to be roughly spherical in shape. This is also why there is a direct relationship between the size of a lump of rock floating through space and its degree of roundness.

However, some Speculative Fiction and Fantasy series, in order to drive home the point that they do not take place anywhere resembling Earth, have their heroes adventuring on a planet with a totally different and often quite improbable shape.

Common world shapes:
 * Spherical - Typically, a world is assumed to be a sphere unless specified otherwise. However, it is somewhat poorly portrayed in video games, where an effectively toroid world is easier to implement. See below.
 * Flat World
 * Ringworld Planet (concave cylinder or ribbon)
 * Dyson Sphere
 * Hollow World
 * World in The Sky
 * Shapes we don't normally encounter - Alien Geometries, shapes with dimensions from four on up, hyperfolds, things only mathematicians and madmen can visualize, etc.

A twist on this is Video Game Geography, type 1, where the world doesn't actually have an odd shape, but the way the programmers implemented the World Map implies that it does.

Interestingly, when "Planet" was given a formal definition (thus demoting Pluto), "big enough to be spherical from its own gravity" became one of the requirements, so any non-sphere planet is not a planet (of course, any such body being discovered in the real universe has a solid chance of leading to a change in definition)

Anime and Manga

 * Prester in Last Exile is.
 * File Island in the last arc of Digimon Adventure is a huge pyramid with several sides, twisted in a spiraling shape.
 * In Tsutomu Nihei's Biomega, the badguys' schemes eventually result in the creation of a bizarre new world which is shaped like a giant worm, tens of millions of miles long.
 * The ending song of the Fighting Foodons anime series reveals the planet everyone is on to be shaped like a soup bowl.
 * An episode of Outlaw Star featured a planet with such a high rate of rotation that it was distorted into an oval spheroid.
 * A probable Shout Out to Hal Clement's novel Mission of Gravity - see Literature folder.
 * Kirby of the Stars for some reason featured a planet shaped like King Dedede in which Dedede was doomed to orbit for eternity at the end of the episode with the Dedede dolls in it, as a result of Kirby swallowing one of said dolls.

Comic Books
"Witness: "Penguin evolution is a myth."
 * In the DCU's Bizarro Universe, Bizarro Earth is shaped like a cube.
 * The Micronauts in the Marvel Comics adaption originated on Homeworld, a planet shaped like a classroom model of a segment of DNA; a dozen spheres linked by cylinders, arranged in two connected rows like a ladder.
 * The Guardians of the Galaxy encountered the Topographical Man, an inhabited planet-sized humanoid.
 * During the Emperor Joker storyline, it is revealed that,  Oddly enough, the Moon seems to remain a sphere.
 * During an arc in Bloom County, Opus is put on trial for teaching "Penguin evolution", in a riff on Inherit the Wind. At one point, the prosecution introduces an expert witness on the subject of "penguin creationism". Unfortunately for the prosecution, the witness is a bit of a Cloudcuckoolander;

Prosecution: "The state rests."

Witness: "Also, the world isn't round."

Prosecution(under his breath to witness): "Save it."

Witness: "Yep, it's shaped like a burrito!""

Film

 * Monty Python and The Holy Grail. See the page quote. Of course, don't take this seriously.

Literature

 * Philip Jose Farmer's World of Tiers took the form of a world-sized wedding cake, just that the layers (tiers) are way wider than they are tall. And the top layer doesn't have a bride and groom standing on it.
 * CS Lewis's unfinished novel The Dark Tower features Othertime, which is presumably spherical, but which the inhabitants believe to be saucer-shaped. (Flat, but you can't get to the edge because gravity drags you back to the center. Of course.)
 * Arthur C. Clarke (Creator)'s short story "The Wall of Darkness" is set on a world shaped like a Klein bottle.
 * The later Xanth books introduce Ida's moon which contains a complete copy of the world except slightly shifted. Naturally Ida exists on that moon and has a moon and so on. All of the shapes from spheres to discs to toroids to dumbbells to spirals to floating islands show up as one progresses down the chain of moons.
 * Don't forget that Xanth itself is the shape of Florida, albeit with more varied terrain. Leaving the magical area of Xanth results in entering Mundania (Earth).
 * The world in Esther Friesner's Majyk trilogy keeps changing its shape, due to being over-saturated with magic. At present it looks like a Moebius strip.
 * Well World is spherical, but the surface and atmosphere are divided into hexagons, with a hundred-miles-tall band around the equator.
 * Atherton: The House of Power is a satellite shaped like a traditional wedding cake with three layers. Except that the layers move up and down unexpectedly.
 * Christopher Priest's The Inverted World takes place in an universe where planets and stars are shaped like hyperboloids of rotation
 * Not Quite Truth in Television: In the early years of the 20th century some scientists magazine writers willing to attribute their ideas to vague "men of science" apparently believed that as the Earth cooled it would assume a tetrahedral shape.
 * In the Culture series by Iain M. Banks, Matter, introduces the Shellworlds. Spherical worlds tens of thousands of kilometers across, with fifteen concentric habitable layers, each a separate world of its own.
 * Robert L. Forward's Rocheworld, two egg-shaped planets orbiting so closely around each other that they share atmosphere, and come to conical points at the ends nearest each other. Oceans can even flow between them under certain circumstances. The oddest thing is that this bizarre world-shape uses real-world physics, and double stars with this configuration have been found.
 * Mandala, by David Bischoff, was set primarily on an icosahedral world.
 * In an early Discworld novel, characters get a glimpse of some other worlds, including one based on the Norse conception of the world as a flat disc surrounded by the Midgard serpent, and one where an enormous tree sits at the hub.

According to The Creator (the guy who made the made the universe) most worlds and universes he makes are flat worlds. There was one universe he forgot to put edges on the planets though...
 * Terry Pratchett's The Dark Side of the Sun has a planet made entirely of water, and two stars twisted into linked toruses.
 * Mesklin in Hal Clement's Mission of Gravity spins so rapidly that it's lens-shaped rather than spherical. Except at the equator, however, the atmosphere is so dense due to the planet's intense gravity that refraction makes it look bowl-shaped. The Mesklinites can "see" that the world curves up around them, so they believe that they live in a giant bowl. They are skilled sailors and map-makers and should know better, however when you are measuring distances on a curved surface, there are two different shapes that will make all the math work out (convex and concave). The Mesklinites choose the wrong one for their maps and never notice. The result is perfectly accurate and usable maps based on a fundamentally flawed premise.

Also the Mesklinites living on the northern hemisphere have apparently never before crossed the equator to the other side and therefore didn't know that they were wrong all along.
 * Unless the air gets less dense as you go down, refraction would make the light curve up, which would make it look more convex than it is, rather than concave.
 * Human kind in Glasshouse by Charles Stross is spread throughout a huge number of space stations and spacecraft in deepspace, all linked together by an even greater number of wormholes. This often results in bafflingly complex geometries and TARDIS-like effects where different rooms and floors of what appear to be a single contiguous building need have no geometric relationship to each other at all, once you enter them. This can make some regions impossible to navigate without computer assistance.
 * In Adam Roberts' novel On, the earthlike (or possible Earth) planet is a sphere, but due to some possible Hollywood Science, gravity has flipped 90 degrees and now works east (spinward?). Therefore, the entire planet is basically a collection of cliffs and sloped plains, the former plains and mountains.
 * After reading the description of the world Katrin created in the Myst novel many geophysicists need to go have a little lie down.
 * Stephen Baxter's short story collection Vacuum Diagrams has two examples. The story "Vacuum Diagrams" features a perfect cube large enough to have its own gravity. Standing on the flat surface, it appears to be hyperbolicly curved, with the horizon ending in four enormous mountains. The stories "Shell" and "The Eighth Room" feature a planet Earth that has another Counter-Earth in a close trojan orbit. Due to Alien Geometry, each Earth appears to be the interior of a hollow sphere, with the other Earth hovering in the center of it.
 * A story in the 1990s incarnation of Amazing Stories was set on a world that was spherical, but with more than 360 degrees of rotation. In other words, if you sail 360 degrees eastward you end up somewhere that has the same time zone as your origin, but which isn't the same place.
 * In Alastair Reynold's novel Absolution Gap, the gas giant Haldora, which is actually  briefly appears cubic when it is shot at.
 * In Greg Egan's trilogy Orthogonal, the entire universe seemingly has the topology of a torus, though the only reason the characters believe this is that it's the only way to make its physics consistent; they haven't actually gone all the way around in any direction.

Live Action TV

 * Castrovalva in the Doctor Who serial of the same name. Revealed as such when the pharmacist is asked to draw a map of the city, and marks his pharmacy as being at the top, and the bottom, and to the west, and to the east, although there is only one shop.
 * Lexx had a ringed planet with an unexplained donut hole through the middle.

Tabletop Games

 * Dungeons and Dragons. The known planes of existence include both finite and infinite flat worlds (including one with two flat, populated surfaces "facing each other"), cubic planets, planets that are giant mountains etc. etc.
 * Ysgard (Chaotic-Chaotic Good) is composed of three layers: Ysgard proper (hovering mountains foth fire on one side), below that is Muspelheim (mountains further apart and fire-side up) and Nidavellir (underground tunnels full of geothermal activity).
 * Limbo (Chaotic) is an infinite shifting storm of the four elements.
 * Pandemonium (Chaotic-Chaotic Evil)is an endless series of caves that acts as a world-sized out-of-tune woodwind instrument that will drive you insane if you stay there for too long.
 * The Abyss (Chaotic Evil) is infinite layers of mind-bending horrors. They never go into detail as to what they look like, but it's not a leap to assume that every world shape is eventually accounted for.
 * Carceri (Chaotic Evil-Evil) is an infinite series of concentric spheres, each of limited size. In First Edition, each plane of Carceri was occupied by an infinite number of planets arranged like strings of pearls, and descending to the next layer took you to a smaller version of the planet you started on (on the first layer the planets were physically connected; each subsequent layer increased the distance between surfaces).
 * Hades (Evil) is three flat, blasted wastelands that meet in the City In The Center
 * Gehenna (Lawful Evil-Evil) is a trio of volcanoes of limited size. In First Edition, it was three infinite flat plains... on which gravity functioned at 45 degrees to horizontal.
 * Baator (Lawful Evil) is shaped like Dante's Inferno--concentric ledges, each of infinite size.
 * Acheron (Lawful-Lawful Evil) is four classic-style dense asteroid belts, each layer with unique asteroid shapes, the best-known of which is just cubes, as far as the eye can see.
 * Mechanus (Lawful) is a continent-sized gear powering smaller gears going off in all directions.
 * Arcadia (Lawful-Lawful Good) is two flat layers, the lower of which is mostly gardens for some reason, and the upper of which has a mountain where the sun spins atop it like a basketball on a Globetrotter's finger.
 * Celestia (Lawful Good), viewed from afar, is an enormous mountain surrounded by an infinite sea of holy water. Those on the mountain view it as divided into seven layers, each smaller than the last, and each of infinite size.
 * Bytopia (Lawful Good-Good) is two layers arranged sandwich-style with a few mountains connecting the two. One layer is domesticated farmland, the other a somewhat harsh wilderness; natives can move from one to the other as they please.
 * Elysium (Good) is the opposite number to Hades, but still flat.
 * The Beastlands (Chaotic Good-Good) are three planes of wilderness: one of eternal day, one twilight, and the last night.
 * Arborea (Chaotic Good) is three flat layers: one an exaggerated realm of incredibly huge mountains and forests of giant trees, one infinite shallow ocean, and one dusty desert.
 * Outland (Neutral), outside of the city of Sigil, has a ring of sixteen cities, each around a gate to one of the other planes. The cities mark the edge of normal space, and one can travel for months beyond the cities and it will only ever take days to return to them.
 * The Far Realms (???), which contains an infinite number of not quite really parallel layers, each of which ranges from inches to miles thick. It's often possible to perceive multiple layers simultaneously. These layers can grow, spawn further layers, breathe and possibly die.
 * In the Planescape setting of Dungeons and Dragons, while the plane of the Outlands is, presumably, a flat world, its most interesting feature, the planar trade hub of Sigil, is built on the inside of a toroid that floats above the spire at the plane's center. the first books even had special rules for getting disoriented when you look up and see more city instead of sky.
 * The Ravenloft setting apparently consists of chunks of landscape adrift in a Mist-filled void. Differs from World in The Sky in that this arrangement is highly unpredictable and tenuous: cross the Misty borders, whether by walking, riding, or even sailing, and it's anyone's guess where (or if!) you'll come out.
 * In Reign, the known world is shaped like two people lying down in a pool of water, with one resting an arm on the other. Rendered in three dimensions. This leads to some unusual properties -- for instance, the ocean is at a 90 degree angle to the shore; gravity is relative so sea travel still works, but boarding a ship can be tricky. A picture is available on the official site, if you're having trouble visualizing it.
 * The setting of Exalted is a rather large Flat World surrounded by Cosmic Horror.

Toys

 * Bionicle: It's eventually revealed that the world Mata Nui guards is

Video Games

 * In Halo you have the titular Halos (Halo 1 and 2), which are ringworlds, the Ark (Halo 3), which is shaped like a flower, and the Micro Dyson Sphere (Halo Wars).
 * Cosmic Osmo has everything from a cardboard diorama to a stellated polyhedron.
 * The world in Phantasy Star 3 was made of six roughly round portions joined by tubes.
 * The Kirby series. This ranges from vaguely acceptable - chunks of rock orbiting each other, a gigantic drop of water - to downright silly. A heart-shaped planet with a smiley face and rings with ribbons on them?
 * The game Meteos pulls off most of the tropes on this page and probably more.
 * Super Mario Galaxy. Pick a shape, any shape. Some worlds are spheres, some are cylinders, and at least one is peanut-shaped. All have gravity perpendicular to the surface.
 * It gets even better in the sequel, which features a planet shaped like Mario's head that's been fitted with engines and turned into a spaceship.
 * In the classic adventure games Relentless and Twinsen's Odyssey, the world in question, Twinsun, is spherical, but exists at the barycenter of a binary system. One that, thankfully, has a rather distant orbit. The result? Tropical poles and a giant frozen "ring" around the equator (and presumably no such thing as night, but that's a different matter.)
 * It is stated in the endgame that some or all of the worlds on which the Might and Magic series takes place . The worlds of MM 4 and MM 5 are the front and backside of a large flat rectangle; playing both games in sequence gives you an extra endgame that (somehow) lets you combine these into a sphere.
 * This was Ret Conned in DMoMM and HoMM4, since the franchise's new owners think such a complex legacy might cause a neuron to accidentally fire amongst their intended audience.
 * The adventure game Torin's Passage is set on a series of concentric hollow spheres; the main character starts the game on the outermost and has to work his way to the inside of the innermost, where he is in zero-gravity and has to make his way around by using a bagpipe to expel air in the opposite direction.
 * The basic structure of the world is similar in the computer RPG Septerra Core, with the addition that the planet has a clockwork core. Each layer is actually a set of disconnected islands that rotates on its own axis. So, you can see lower layers in the gaps between islands and through holes, with each layer receiving less and less sunlight through the gaps as you get lower (and thus each layer becomes increasingly dark and hellish as you go down). A major plot point involves the rare occurrence of the layers lining up so that a single beam of sunlight reaches the core.
 * The world map visable during the character select screen of Darkstalkers appears to be some kind of triangular mobius strip.
 * Tales of Eternia (Tales of Destiny 2 in the US) has a universe consisting of two flat edge-warping worlds that face one another, so each world is effectively the other's sky. A sun dispensing variable illumination is lodged in an energy barrier that keeps the two worlds apart.
 * Elric at the End of Time, by Michael Moorcock has two landscapes, each hanging in the other's sky. Elric is astounded by the sight, while to the ultra-powerful yet rather shallow inhabitants of the End of Time it's about as remarkable as a new patio. A Rodney Matthews illustration of the story was designed to be viewed both ways up, effectively giving two illustrations for the price of one.
 * Spore allows for cube-shaped planets to be randomly generated.
 * In Xenoblade, the world is entirely made up of the bodies of two Physical Gods who either killed or incapacitated each other in combat. There is no world beneath them and no stars above them.
 * Discussed in the Blazing Dragons (which oddly enough, with the page quote, was written by Terry Jones). At one point the smart knight announces he was rewarded with a ribbon for deducing the world was the shape of a duck...he was in an insane asylum at the time, take that as you please.

Webcomics

 * The world of Rice Boy is a typical flat disk world spinning like a coin, with the notable deviation that
 * Triangle and Robert's four-dimensional "hypertaco" Earth is not healthy to visualise.
 * The Imaginary Universe in MS Paint Adventures: Problem Sleuth consists of two seemingly-spherical lands on opposite sides of a typical spatial void containing a way-small sun and moon and at least one Floating Continent, the two worlds connected by a single gigantic 133,331-story cathedral. It is either heavily implied or outrightly stated that the Imaginary Universe is much, much "wider" than it is "tall". If none of that is making sense, there's a picture of it here.
 * Schlock Mercenary
 * The world Zoojacks in is literally shaped like a pair of toy jacks.
 * Also the Enireth-built Tinth, which are shaped like giant sandwiches. Yes, the strip linked to refers to the Tinth-Philkra system, but strictly speaking it's the Philkra system, and was renamed by popular mistake as everyone assumed the Tinth-Philkra Dialogues were named for the system, rather than the hypernet node of origin (on Tinth-III, in the Philkra system).
 * Pastel Defender Heliotrope
 * Some toroid-shaped worlds are seen briefly, but not visited.
 * Also seen: worlds shaped like endless living strands, worlds shaped like... this, and worlds shaped like scary alien tendrils.
 * Unicorn Jelly:
 * Triangular world-plates with triangular lakes in the middle, each orbited by a tiny sun and moon. Basically, Jennifer Diane Reitz loves this trope; her sci-fi setting spans multiple universes, and each has its own laws of physics, which mostly manifest in bizarre world shapes.
 * Illustrates that a sphere can be a bizarre world shape. A scientist from an alien universe, where gravity as we know it doesn't exist but where there is an absolute "down", comes across a fragmented description of our world. He speculates that the spherical shape of our planet must lead to a very stratified society, where the rich all live in the "safe" areas closest to the top of the sphere, and lower classes live further down the slope, where they must deal with the risk of slipping off.

Western Animation

 * Captain N: Some of the worlds in had unusual shapes, some inspired by the games they were based on (such as Mount Icarus being mountains and plains suspended above the clouds and Faxanadu being a floating continent dominated by its World Tree) and others with fuzzier inspirations (such as Hyrule being an Earth-like sphere enclosed in some sort of crown-mountain-floating rock thing).
 * Transformers
 * Planets in the first two seasons of the original series were spheres. Come The Movie we are introduced us to Junkion, which is for all intents and purposes, a planet with a surface made of used chewing gum pulled taut over a large area, and Quintessa, which looks like a sphere, but has several large, almost blade like, masses of continent jutting out from the equator.
 * Cybertron is round in the sense that a massive katamari is round. It's like the skyline of every major city on Earth wadded up into a round chunk of skyscraper.

Real Life

 * Though technically not a planet, Achernar is a star that is over twice as wide as it is tall, due to it spinning so fast.
 * Haumea, a dwarf planet in the outer Solar System which is distorted into a long ellipsoid by its very fast rotation.
 * Asteroids. These are too small to be pulled into spheres by their own gravity, and double as Shattered Worlds. Asteroid 216 Kleopatra is shaped like a dog bone.