Structure

Every specific group of blocks purposefully formed in Minecraft based on coding is part of a natural structure.

The Overworld
The Overworld contains numerous generated structures, at a wide variety of scales.

Terrain
Biomes dictate the shape and height of the world. At this stage, the ground is made mostly of stone and stone variants, with water filling in most empty spaces below layer 63, with exception for structures.

Mountain
Mountains are hills with extreme slopes and cliffs. Mountains can sometimes have caves through them. On an amplified world, mountains are extremely common in all biomes except ocean and swamp biomes.

Floating "island"
Floating "islands" are structures that float in midair that are not connected to the ground, the sea, hills or cliffs. Floating "islands" are normally just random pieces of floating dirt and stone found near cliffs, but on rare occasions they can be large, floating structures that even have springs and trees on them. Floating Islands are most frequently found in the Mountains, Snowy Tundra, Snowy Mountains and Mushroom Fields biomes, but can be found anywhere. Floating Islands are very common in an amplified world.

Hollows
Hollows are the opposite of floating islands. They look like caves, but they have nothing to do with cave generation (although they may intersect with them). When there are many overhangs, they close together and create a hollow. They have exactly the same floor as the terrain above, depending on the biome that they are located in, unlike caves. Hollows have no specific floor. Grass blocks can generate inside too, and interestingly will survive without light. When they generate under the sea level, they are filled with water. They are extremely rare in the default world, but can be found far more commonly in certain customized worlds.

Hill
Hills are randomly generated pieces of land in the map. Like stairs, hills are always traversable to their lowest point by virtue of the algorithm which generates them; there is almost always a place on each level from where the next level can be accessed, meaning that the player can climb a hill one level at a time until they reach the top. Cases where this is not true are rare.

Beach
Beaches usually generate next to oceans and cover all nearby shorelines. They come in two different varieties: sand beach and stone beach. Sandstone is located below sand in sand beaches. Stone beaches are usually steep cliffs that lead straight into the water.

Surface layer
The uppermost layers of the terrain are converted to a biome-dependent material: usually grass blocks and dirt, or sand in deserts and beaches. Podzol is found in giant tree taiga, mycelium in mushroom field biomes, and red sand is found in the badlands biome. Sandstone is generated under sand.

Basin
Occasionally, instead of being converted to dirt or sand, the top layer is stripped away, leaving a 'basin' of bare stone. They bear some resemblance to a geological 'shield' (an area of tectonically stable rock that has been exposed to prolonged erosion due to its very old age; it is distinct from the geological term "basin"). They seem to be more common in forest or plains, and are occasionally seen filled with water. Commonly, minerals can be found in these, generally coal ore and iron ore. If generated in a Badlands biome, gold ore can also be seen.

Ocean
Oceans/Seas are huge bodies of water with every single water tile being a source block. The ground can rise high enough to produce small, relatively barren islands.

River
Rivers are long "strands" of water that cut through or separate biomes. They do not have a current. Patches of sand and gravel are seen commonly dotting the banks of the rivers, and clay settled at the very bottom. In some cases, rivers will generate higher than normal, producing a dry riverbed, sometimes with occasional small water patches.

Lake
Lakes are small bodies of liquid. Water lakes, which are small pools of water springs, can generate above sea level or inside caverns. They can also generate isolated underground, connected to no other structures whatsoever. When in a winter biome, these small lakes are never initially frozen but will turn to ice if exposed. The lakes can also be composed of lava; however, lakes of lava are much rarer. Lava lakes found at the surface are surrounded by stone (which can be replaced by ore veins such as dirt, gravel and coal). Both types of lake generate with a small air pocket above them, which may result in floating sand, floating snow cover or even the top 2/3rds of trees above the lake. Lava lakes may cause trees to burn away.

Coral reef
Coral reefs are structures that generate in warm ocean biomes. They consist of multiple clusters of coral blocks, coral and coral fans. These clusters come in a wide variety of shapes, sizes, and colors, ranging from a few blocks of brain coral on the ground to large tree-like structures of fire coral.

Cavern
Caverns are caves and tunnels that are automatically generated under the ground in various places, composed of primarily stone and ores. Flooded caves are also able to generate in ocean biomes.

Ravine
Ravines are tall, thin trenches that generate either underground or at the surface, and extend 30 - 50 blocks downwards or to bedrock level in the Bedrock Edition. Ravines can spawn in the ocean making it look like underwater trenches.

Abandoned mineshaft
Abandoned mineshafts are structures generated underground (partially above ground in badlands biomes) which consist of branching mining tunnels with wooden supports and broken rails passing through it. They are the only places where cave spider spawners and minecarts with chests can be found naturally.

Stronghold
Strongholds are underground structures made up of stone bricks, monster eggs, and iron bars. They consist of many rooms, most notably libraries and end portal rooms. Although they are very rare, they can be found much more easily by using an eye of ender.

Small structures
The quantity of most of these features (aside from dungeons, mineral veins, and springs) is biome-dependent; not all features can be found in every biome.

Dungeon
Dungeons are small, mostly underground, one-room spaces bordered by moss stone and cobblestone, and typically contain chests with rare items, and a monster spawner in the center, which will spawn zombies, skeletons, or spiders.

Mineral vein
A mineral vein is a natural deposit of ores. Players can come across these veins in caverns or anywhere where there is natural stone. Underground deposits of dirt and gravel are generated in this step, followed by the more precious ores: coal, iron, gold, redstone, diamond, emerald (in mountains biomes) and lapis lazuli. They can only form in stone, and do not replace each other or any other block. However, there is one exception: other ores can replace andesite, diorite and granite. Note that two or more mineral veins can form next to each other and make it look like a mineral vein made of more than one material.

Tree
Trees are common structures created both during world generation and by players (grown from saplings). They are made of wood and leaves, and in Bedrock Edition and Legacy Console Edition, might have vines or mushrooms (as dying trees and fallen trees respectively).

Huge mushroom
Huge mushrooms are structures made up by mushroom blocks in the shape of a mushroom. They naturally generated in mushroom fields, swamps, and dark forests, and will also generate if the player uses bone meal on a mushroom.

Spring
Springs are randomly generated blocks of either lava or water that act as a source of their respective material. While both can be found on the vertical side of stone blocks above the surface, lava springs are more often found underground beneath layer 32 in caverns and mineshafts. They do not generate above a certain Y altitude.

Desert well
These well-like structures built of sandstone blocks and slabs generate only in the desert biome. They have a 1/1000 chance to be generated in any desert chunk, which makes them a rare sight. It is possible for a well to generate around a cactus. The well structure will still generate with the "Generate Structures" option disabled. In Bedrock Edition, it is common to find two desert wells spawning in the same chunk.

Moss stone boulder
These structures are meant to represent boulders, made entirely of moss stone. The arrangement of these structures varies greatly. They can be found dotted around areas of the Giant Tree Taiga biome. Moss stone boulders are quite rare, due to the giant tree taiga biome's rarity.

Ice spike
Ice spikes are tall spires made of packed ice that can only be found in the snowy tundra biomes. There are two variants of ice spikes: one is short and thick, and the other is extremely tall and thin.

Fossil
Fossils represent the remains of giant extinct creatures, and are composed of bone blocks, with random blocks removed and some of them replaced with coal ore. They were made with NBT structure block format and they have NBT files of different types of fossils in minecraft.jar/data/minecraft/structures/fossils. Fossils randomly generate 15-24 blocks (i.e. at y coordinates ranging from 40 to 49) below the surface in deserts and swamps, including the "Hills" and "Desert Lakes" variants. Each chunk has a $1/64$ chance to generate a fossil. They may generate as one of four different variants of skull or one of four different variants of spine.

Buried treasure
Buried treasure structures consist of a single chest buried in the beach sand or gravel, with random loot in it.

Shipwreck
Shipwrecks are structures that generate on the floor of oceans or beaches. They are made up of wood materials, and contain 1-3 loot chests. They can generate sideways, upside-down, or upright.

Iceberg
Icebergs are structures that generate in frozen oceans and their deep variants. They consist primarily of packed ice with a little bit of ice and blue ice, and will often be topped with snow. They are the only place where blue ice can be found naturally. Icebergs generate in a wide variety of shapes and sizes, ranging from small "islands" to giant mountain-like ice structures. They can also generate with "cave-like" holes in them, which sometimes reach to the other side of the iceberg. Polar bears can also spawn here, much like other cold biomes.

Buildings
Buildings are naturally generating structures that form above ground. They can contain valuable treasure, but traps and puzzles as well.

Village
Villages are generated in desert, plains, taiga, and savanna biomes, and are a site for villagers, with whom the player can trade. They are composed of a random selection of various buildings and farms.

Desert temple
Desert temples are pyramid-shaped structures found in deserts, composed of mainly sandstone and stained terracotta. There is a hidden chamber in the middle of the temple, containing 4 treasure chests and a TNT trap.

Jungle temple
Jungle temples are found in jungles, and mainly consist of cobblestone and moss stone. There are three floors, the bottom floor containing treasure chests, tripwire-activated traps and a puzzle consisting of three levers that must be pulled in the correct combination to reveal one of the chests.

Witch hut
Witch huts are structures that generate in swamp biomes that have the ability to spawn witches. They are composed of several types of wood materials, and contain a crafting table, cauldron, and flower pot inside.

Woodland mansion
Woodland mansions are massive house structures that generate in dark forests, containing a wide variety of rooms. They are the only place where evokers, vindicators, and vexes spawn naturally (but only once).

Ocean monument
Ocean monuments are underwater structures that generate in deep oceans. They are composed of all three variants of prismarine and sea lantern, and are the only places where guardians and elder guardians spawn naturally.

Igloo
Igloos are structures that generate in snowy biomes. The structure consists of the igloo house and in some cases, a basement hidden under the carpet.

Underwater ruins
Underwater ruins are clusters of many different blocks that generate underwater in ocean biomes, as well as on the surface on beaches. They come in many different variants - the cold variants consist primarily of stone bricks and the warm consist primarily of sandstone.

The Nether
The Nether, though equally vast, contains far fewer types of generated structures than the Overworld.

Lava sea
Lava seas are found at and below level 30 in the Nether. They make a large portion of the Nether, and are extremely common. They can stretch for hundreds of meters in any direction, and are usually bordered by netherrack (or more rarely soul sand).

Nether fortress
Nether fortresses are very large complexes made mainly of nether bricks (with added nether brick fences and stairs to be found). They contain blaze spawners, nether wart farms, and loot chests in them.

Glowstone clusters
Glowstone clusters are typically veins of glowstone that can be among the hardest natural materials to harvest that don't require digging. They form in coral-like structures on the underside of hanging Netherrack, so they are often found on the ceilings of the Nether, where they provide light along with the ever present lava.

Other things located in the Nether
There are areas of soul sand and gravel around layer 64, veins of nether quartz ore, large "veins" of magma blocks and "hidden lava", which is a single block of lava generated randomly between netherrack.

The End
The End is the final and most barren dimension, with very few types of significant structures, until after defeating the Ender Dragon, which will open gateways to more structures.

The Central Island
The center of the End is a large, asteroid-like island composed entirely of end stone, floating in the void. At a distance of 1000 blocks away, an endless expanse of more islands begins, away from the main island. These consist of large islands, about the size of the main island, and smaller ones, which are usually very thin and small.

Obsidian pillar
Obsidian pillars, also known as obsidian spikes or obsidian towers, are tall, tower-like structures that generate in The End in a circle around the fountain. The End crystals on top of each one will heal the Ender Dragon.

Obsidian platform
The obsidian platform is a 5 by 5 square of obsidian that is generated once a player enters the End. (Note that if the obsidian is destroyed, or if a block is placed on top of it, when the player enters the End, the obsidian will be restored and any blocks on top of it will despawn.) Obsidian platforms generate at X, Y, Z = 100(100.5), 48, 0(0.5), mostly far away from the island, making it tough to get there. Players who enter the end will spawn at X, Y, Z = 100, 49, 0 and the other entities that enter the end will spawn at X, Y, Z = 100.5, 50, 0.5, the middle of platform and 1 block higher than the platform.


 * Sometimes the platform generates inside a case of end stone. It will remove enough end stone so that the player can walk around.
 * Occasionally the platform will generate in midair.

Exit portal
The exit portal is a structure that generates when the player goes to the End. It will activate after the player has killed the ender dragon, allowing them to go back to the Overworld.

End gateway portal
The end gateway portal is a portal to quickly get to the outer islands of the End. It can only be accessed via a one-block gap, meaning that ender pearls or an elytra is required to use it.

End city
End cities are tall castle-like structures that generate in the outer islands of the End, consisting primarily of end stone bricks, purpur blocks, and end rods. They are the only places where shulkers can be found.

End ship
End ships are common floating structures that are often generated alongside end cities. They are the only place where the elytra and the dragon head can be legitimately obtained.

Chorus tree
Chorus trees generate on the outer islands of the end. They are formed in tall, coral-like patterns.They consist of chorus stems and chorus flowers. A chorus flower will generate at the top of each branch. They are the only source of chorus fruit and chorus flowers. You can grow a new chorus tree by planting a flower on a block of endstone.

Return portal
Return portals are end gateway portals that generate randomly throughout the outer End islands. These will teleport the player back to the center island's spawn platform.

Technical details
Structures are generated for a given chunk after the terrain has been formed. The chunk format includes a tag called TerrainPopulated that indicates whether structures whose point of origin is in that chunk have been generated. If it is false or missing, they will be generated again. Structure generation is based on what is already in the chunk, so (for example) flagging a chunk that has already been populated for repopulation will approximately double the amount of ore in it.

When structures are generated, they can spill over into neighboring chunks that have been previously generated. Thus, a tree at the edge of the generated world (and probably only visible using external tools) may be overwritten by a lake before you reach it. It is also theoretically possible for two worlds generated with the same seed, from the same version of Minecraft, to differ slightly depending on the players' travel routes, because the order in which chunks are generated may determine which of two conflicting structures will overwrite or suppress the other.

Trivia

 * In previous versions, before snow cover was solid, a lava lake with floating snow cover above it could be a deadly trap before the snow melted.
 * The smallest possible fully-grown chorus tree (assuming the growth is not obstructed) would have 5 chorus plants.