Trapdoor

The Trapdoor (Also known as Hatch) is a block used as a horizontal door.

They are placed over a single-block hole (but can be placed over a solid block as well) with a solid block directly adjacent. When activated, they will then open by flipping upwards toward the adjacent block. If that block is destroyed, the hatch is as well. Due to this restriction it is currently not possible to create a flat floor with a hatch opening downwards.

Just like doors, hatches can be activated by redstone circuitry. When placed outside, rainfall, water and snowfall do not pass through a hatch, but light is let in through the four gaps on its surface.

Redstone
As with doors, hatches can be controlled with redstone circuitry. A charge will cause the hatch to change its state, from either on or off, depending on it starting state.

Drawbridge
If you place the hatches in a trench in this fashion:

You can create a fairly good drawbridge. You can extend it lengthways, but not widthways. However, it's possible to walk on the ledge of an opened hatch if there is enough space above it. Additionally, since the Trapdoor acts as a half block for space, it is not possible to create a walkable path over a trapdoor without at least 2 open blocks above the block occupied by the Trapdoor. A walkable path over a trapdoor is therefore vulnerable to ledge walking.

Underground Entrance
You can make an useful entrance to underground using hatches. It can be controlled by Redstone using Redstone Dust, Redstone Torches, and possibly if you want it automated Redstone Repeaters. Obviously, you can use different objects that give charges instead of Pressure Plates.

Bugs

 * Hatches seem to break faster using a pickaxe instead of an axe, like wooden slabs.
 * Minecarts do not collide with hatches whether they are open or closed.
 * Hatches may not be placed next to double half blocks.

Trivia

 * Much like the Piston is based on a mod developed by Hippoplatimus, the hatch is very likely based on a mod from DJoslin. (http://www.djoslin.info/trapdoor.php)
 * Sand and Gravel, if dropped onto a hatch will break into items (similar to how sand or gravel falling on a torch will do the same).
 * Liquids (water and lava) cannot fall through a single hole hatch. The hatch counts as a block and can't have something else in it, even in it's open state.  Hatches will stop the block above it whether it's open or closed.