Dropper

The dropper is a block that drops a random item from its inventory as an entity (as if it were dropped by the player) each time it is powered. If there is a block with an inventory immediately in front of the dropper when it is powered, it will instead store the item within the inventory associated with that block. A dropper can drop items through a glass block in front of it. Droppers click when powered if empty or ejecting items into air, but are silent when successfully pushing items into other inventories.

This is in contrast to a dispenser, which behaves differently with certain items, such as firing projectiles, pouring liquids from buckets, and spawning mobs from spawn eggs. Dispensers also do not store items in container-type blocks, rendering items stuck somewhere in between.

The hopper is useful for moving items sideways or downwards, pulling items from containers, and doing all that without intervention by redstone circuitry; the dropper, by contrast, is the only block that can push items upwards into a container block. When multiple droppers are arranged vertically, they can be configured to act as an upwards elevator for items. Droppers also cause significantly less lag in SMP than hoppers, even when running on a fast clock.

Trivia

 * By placing droppers so that they feed into each other, similar to a hopper pipe, and powering each of them and updating them with a 1 tick clock, an extremely fast transport system can be produced, with the advantage of going all 6 directions, at a speed of 10 blocks per second. This means that if you have a 100 block long dropper pipe, items going in on one end will pop out the other end in only 10 seconds.
 * This is twice as fast as a hopper pipe, however, two hopper pipes side by side take up less space, and make no sound.
 * This is also only half as fast as an ice-and-water pipe (water running across ice, with a sign behind every water source to ensure items only flow in the correct direction), which also takes up less space, and does not produce excessive updates, but only works horizontally and requires Silk Touch to create in Survival (unless built in an icy biome, or if the ice is pushed to the construction site via a piston train).
 * Like dispensers, droppers are triggered whenever an adjacent block is powered by redstone.
 * When powered there is a delay of 2 redstone ticks (4 game ticks) before a dropper fires.
 * Dropping a block directly into a cobweb placed in front of it will mean that the time for the block to pass through the cobweb will be approximately half of the delay for dropping the block on top of the cobweb. This is useful for a 10-12 second delay redstone trigger.
 * When originally introduced, the inclusion of a hopper in the crafting recipe arguably made this the most complicated object in the game to craft, as it required three different things in order to be crafted, including the hopper, which required another crafted object, a chest, to make. In other words, making one dropper from the basic required materials was a three step process.
 * As of yet, the dropper does not exist in the Xbox 360 or PS3 Edition.