Trapdoor

A trapdoor (also known as hatch) is a block used as a horizontal door that fills one block space. It is operated by clicking on the trapdoor, or with a redstone signal. They can only be placed on the side of a solid block. When activated, they will open by flipping towards the block they are attached to. If that block is destroyed, the trapdoor will pop off. When placed outside, rainfall, water, lava, and snowfall do not pass through a trapdoor, but light is allowed to shine through.

Trapdoors are $3/16$ of a block in height.

Usage
Most obviously, they are a door in the floor, useful for preventing accidental falls or mob entry into a hole. They also block water or lava, whether open or closed. They can also be used for decorative purposes.

Trapdoors can be used as a less unsightly method of restraining boats at a dock than doors. It's also possible to create a distributor with a vertical succession of trapdoor linked with redstone. They can also be used to create gates, since they stop horizontal movement as well. Similarly, they can be used to create a gate for a counter-top (such as can be found in a bar or restaurant).

As with doors, trapdoors can be controlled with redstone circuitry. A redstone current (on-edge) will cause the trapdoor to open. A trapdoor can be closed not only by the redstone current turning off, but by either placement or removal of uncharged redstone which could (if charged) power it.

Data values
Wooden trapdoors have an ID name of. For iron trapdoors, it is. A trapdoor stores the block face it is on, whether it's on the bottom or top half of a block and whether it's open in its block data. Trapdoors also have block states, which is expected to replace the block data in a future Minecraft version.

Video
Note: the video for wooden trapdoors is out of date.

Trivia

 * Sand and Gravel, if dropped onto a trapdoor will break into items (similar to how sand or gravel falling on a torch or cart track will do the same).
 * Certain mobs, such as sheep, cannot jump onto a block with a trapdoor in the closed position on top. This allows you to make pens that animals can walk into but not out of easily.
 * Like doors, trapdoors are not flammable and do not burn.
 * When attached above a block of lava, the trapdoor will appear to catch fire and set adjacent blocks on fire. This makes trapdoors unsuitable as disposal lids unless surrounded by flame-proof blocks. However, the trapdoor will not be destroyed from fire damage, even stimulating fire generation where it normally doesn't appear naturally.
 * Trapdoors will not prevent you from accessing the contents of a chest if the trapdoor is in the closed state directly above it. This means that they are just like any other door and allow you to interact with objects on the other side even if the trapdoor is closed.
 * If you put a trapdoor on a lava block, the lava will disappear and the trapdoor will not be burned. This allows the creation of paths.
 * Trapdoors can be used as ladders by placing them one above each other down a hole. Then hit them open to go down, and hit them closed to go back up.
 * The trapdoor as a dropped resource used to be much bigger than other resources. This has been fixed in Beta 1.8.
 * Trapdoors can be used as fuel in a furnace but burn only as much as a wooden plank.
 * Trapdoors can be pushed by pistons if there's another block for it to connect to or if the block it is currently connected to is pushed with it.
 * Although zombies are able to destroy wooden doors on hard mode, they can't destroy trapdoors.
 * Walking on trapdoors placed on ice makes walking faster, while sprinting on trapdoors on ice makes the player run faster than a minecart.
 * If you remotely open a trapdoor while a mob is standing over it, it will fall through the door. This makes for an effective trap in front of a vulnerable entrance.
 * A trapdoor can muffle the sound of weather.
 * Trapdoors do not block redstone signals going up under them.
 * Two trapdoors placed within a 1x2 doorway/opening, in the open position, makes for a very narrow entry.
 * A trapdoor is effective for building underwater, since water does not pass through it.
 * If a trapdoor is placed above a ladder in the closed position, you will fall through it and have to open it to get back up.
 * It is possible to jump from a trapdoor placed on the upper part of one block to one placed on the lower part of a block placed two blocks higher. This makes it possible to build a staircase past any block (or void) that a ladder cannot be attached to (such as a fence).
 * While regular trapdoors require 6 wooden planks to craft, iron trapdoors only need 4 iron. This is to avoid a conflict with the Iron Bars recipe.
 * In the future, trapdoors might have different variants depending on the wood used to craft it.