Dispenser

A Dispenser is a special block available since Beta 1.2. When right-clicked, a menu allows you to place items inside it. Each time the block receives power from a redstone circuit, a random item from its inventory drops out.

Unlike chests, when a dispenser is destroyed, the items inside are gone forever. Notch has stated that this is a bug:.

Tutorial
An introductory video tutorial can be found here and here. An automated turret tutorial can be found here.

Crafting
When placed, the dispenser faces the player (it will dispense items towards where the player is standing).

Dispensing
Most items placed in a dispenser will simply be ejected as items and land 2-4 blocks away if on level ground. Arrows, eggs, and snowballs that are stored inside the dispenser are instead fired out (as if they were right-clicked in your inventory). Arrows will cause damage (and cannot be picked up, like arrows fired by skeletons); eggs and snowballs break with all the usual effects.

Unlike most other redstone-triggered devices, it may be triggered by redstone wire placed up to one block adjacent to it as well as running directly into it; therefore a single redstone wire can trigger up to 5 dispensers in a cross pattern. This allows for easy creation of large walls of dispensers.

When a dispenser dispenses an item, it emits a clicking sound and a puff of smoke. If it is empty when activated, it emits a slightly higher-pitched click.

A dispenser will not work if it is placed underwater, unless all sides but the face are covered with a block.

If the face of the dispenser is covered by a block, and the dispenser is facing west or south, fired items will pass through the block.

Trivia

 * The Dispenser uses the same texture as the Furnace on all sides except the face, which has a unique texture.
 * Interestingly, the texture file for the dispenser menu is named "trap.png", possibly because it was originally designed for making arrow traps.