Dragon Egg

The dragon egg is a decorative block, or a "trophy item" in Survival mode.

Obtaining
A single dragon egg is generated on top of the exit end portal when the first ender dragon is defeated. Dragon eggs cannot be mined directly, as trying to mine it will cause the egg to teleport. However, the egg does not teleport if there aren't any air blocks available for it to teleport to, which allows it to be mined. It drops as an item when it falls into a non-solid transparent block, or when pushed by a piston.

Spawning and killing more dragons will not generate additional dragon eggs.

Teleporting
To cause the egg to teleport, press while in Survival or Adventure mode (press  in Creative). It teleports to a place nearby (up to seven blocks vertically and fifteen blocks horizontally), creating the same particles as endermen. It may teleport into the air and subsequently fall to the ground.

Usage
The dragon egg, if there is no block below it, will fall until it lands on the next available block. When it is being affected by gravity and falling, it exhibits a smooth falling animation.

It does not suffocate mobs or players when it falls and covers them.

The dragon egg can be placed on a non-solid block without falling.

Unlike other falling blocks, when the dragon egg is floating, it doesn't have particles underneath.

Light source
Dragon eggs emit a light level of 1.

Trivia

 * The writer of the Minecraft comic WonderCraft, Samcube, was requested by Mojang to create official Minecraft posters. In part of these works, one can see an area with an ender dragon and a chicken on top of a huge mushroom. In the same scene the dragon egg is visible near the chicken.
 * The dragon egg can be considered the rarest block obtainable in Survival due to the fact that it only spawns once per world.