Structure

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

Hills
Hills are randomly generated pieces of land in the map. Like stairs, hills are always traversable to their highest point by virtue of the algorithm which generates them; there is 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.

Floating "Islands"
Floating "islands" are structures that float in midair that are not connected to the to the ground, the sea, hills or cliffs. Floating "islands" are normally just random pieces of floating dirt found near cliffs, but on rare occasions they can be large, floating structures that even have springs and trees on them. Floating Islands are usually found in the "Extreme Hills" biome.

Beaches
Beaches usually generate next to oceans or lakes and cover all nearby low elevated shoreline. They come in two varieties: sand beach and gravel beach. Sandstone is located below sand in sand beaches. Gravel beaches have no such border and thus pose dangers of falling into caverns located right underneath them. Beaches do not generate as of 1.0.0.

Lakes
Lakes are small bodies of water in which the player is able to swim, and are a large collection of water spring blocks. Lakes can now be generated above sea level or inside caverns, and are small bodies of water surrounded simply by dirt. When in a winter biome, these small lakes are never initially frozen but can turn to ice when it snows. These lakes can also be composed of lava; however, lakes of lava are more rare. Lava lakes found at the surface will be surrounded by gravel, stone, and coal ore.

Springs
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. Both of these sources can be collected and repositioned via the use of Buckets. When coming into contact, Water will turn Lava springs into Obsidian; however, if the Lava is not a spring, it will form only Cobblestone. Springs can only be found in Alpha, Beta, and Infdev. Fluids behave differently in older versions.

Trees
Trees are the structures created both by the automatic generation of the map, and by players (they grow from saplings). They are built out of trunk blocks and leaves. When generated by the map, they are frequently found in groups, in the style of a forest. Trees can range from small trees, often found in groups, to large trees that may require several minutes to harvest. In Beta 1.2 Birch trees and pine trees may be found, and in Beta 1.5 birch and pine saplings were introduced. See the tree article for more information.

Caverns
Caverns are caves and tunnels that are automatically generated under the ground in various places. They can be useful for several things, such as finding dungeons, and creating underground structures. Caverns are composed mostly of stone, but frequently contain gravel, dirt, bedrock, water, lava, and small amounts of ores and sand, (depending on your biome).

Mineral Veins
A Mineral Vein is a natural deposit of minerals. Players can come across these veins in caverns, mines, or anywhere there is stone. Six minerals can be found in the game, these include Coal, Iron, Gold, Redstone, Lapis Lazuli, and Diamond. When mined with a pickaxe, gold and iron will drop an associated item or a block that needs to be smelted in order for it to be crafted into items or blocks. Lapis Lazuli, coal, redstone and diamond will drop items that can be used immediately.

Dungeons
Dungeons are small, mostly underground, one-room spaces bordered by Moss Stone and cobblestone, and typically contain chests with some satisfactory loot and a hostile Mob Spawner in the center, which guards the chests. Dungeons are often open to a cave, or more rarely even to the surface. Dungeons together with Strongholds are the only place to find apples, saddles, Mob Spawners and Cocoa Beans.

Rivers
Rivers cut through terrain and attempt to join up with ocean on the other side, but will sometimes loop around to the same area of ocean. They have no current. Rivers have also been known to be a reliable source of Clay.

NPC Villages
NPC Villages are generated on flat lands and are a site for NPCs. They are composed of several different houses, farms and often a smithy and/or a tower. Currently they spawn NPC Villagers in the area around the village. They are, as of Minecraft 1.0, inhabited by Villagers.

Ravines
Ravines are tall, long structures, about 5-20 blocks in height and variably long. The width is barely a few blocks, usually no more than 5, sometimes making ravines hard to navigate from below because the ravine could go on the opposite corner of a block. Ravines can connect to caves, dungeons, and, due to the large surface area of their walls, may have water/lava flowing down them.

Ravines may also have small ledges along the top, which are possible to travel along. Ravines can be found at any level, and also scarcely appear on the world surface, forming canyons. Such canyons do, from time to time, appear underwater where safe entry is possible. [ In this video, at around 4:10, the player dives under the ocean to explore an underwater canyon and successfully resurfaces at the end.] It is also possible for multiple ravines to join together to form a larger network of tunnels/caverns, due to the way that the terrain is generated. Ravines commonly contain useful minerals, such as Coal and Iron in ravines at or near the surface, and Gold and Diamond in ravines further down from the surface. Lava and Water are also common.

Strongholds
Strongholds are structures that contain multiple rooms, doors and other aspects. Stone Brick, Mossy Stone Brick, Cracked Stone Brick, Doors, and Iron Bars are the materials that make up the strongholds. They also contain silverfish and silverfish spawners, which one should be careful of when digging around in them. Portals to The End are found in specific rooms in strongholds.

Lava Sea
Lava Seas are, as the name suggests, great oceans of lava which 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 Fortresses
Nether Fortresses are very large complexes made mainly of Nether Bricks. Nether Fortresses can often tunnel through Netherrack, and the inside of the tunnels will be cleared of Netherrack by the terrain generator. You can find Blaze spawners and Nether Wart inside.

Obsidian Spikes
Obsidian Spikes are structures that spawn in The End. They appeared with The End in Beta 1.9 Prerelease 4. No part of them are in the ground; there is no obsidian below the lowest block of obsidian you can see without digging. Ender Crystals will spawn on top of each one to heal the Enderdragon.

Oceans
Seas/oceans were huge bodies of water with every single water tile being a spring. Prior to the Adventure Update, oceans were generated as part of the terrain generation algorithm, but since then they are part of the Ocean biome.

Cliffs/Extreme Hills/Mountains
Cliffs are carved into hills, and sometimes have caves protruding into them. These caves contain the same blocks which one would find at the same layer in the hill they are carved out of. This may include Ores, Stone, Gravel, Sand, Sandstone and Dirt. As of Beta 1.8, these no longer generate randomly, but are instead part of the Mountain biome.