Dragon Egg

A dragon egg is a block that spawns on top of the bedrock portal created by the defeat of the Ender Dragon in The End. When the player clicks the egg, it will teleport several blocks away (in Creative mode, it will break instead). They currently have no explicit purpose, but are tricky to collect. The preferred way to pick up the egg is to use a piston to push it off of the bedrock pillar atop the portal, causing it to drop as an item that can be placed in the player's inventory. The portal underneath should be covered with blocks, however, before the piston is powered or else the egg will fall into the portal. The player can also fill a large area around the portal with torches and hit the egg. When the egg teleports, it will fall on top of a torch, break, and drop as an item.

They currently have no purpose, other than as a trophy or decoration.

On March 13th, 2014, Dinnerbone tweeted about that he might add a Dragon Egg feature in his "Ultimate Plan", but he hasn't discussed this with the Mojang team yet.

Behavior
Clicking on the egg in survival or adventure mode causes it to teleport to a place nearby (up to seven blocks vertically and fifteen blocks horizontally), creating the same particles as Endermen, Nether Portals, Ender Pearls, and Ender Chests. It may teleport into the air and subsequently fall to the ground. You may want to bring a piston with you to collect the egg as an entity or item in your inventory. Or you could click the egg once to make it teleport to an end stone underground, then place a torch one block below the egg and then simply remove the block above the torch which will make the egg fall on the torch and drop as a resource.

However, the egg does not teleport if there aren't any air blocks available for it to teleport to. This allows for the egg to be mined directly.

Like Sand, Gravel, and Anvils, Dragon Eggs fall when unsupported (due to the fact that they are affected by gravity), and if they land on a non-solid block, (such as a Torch, Slab or Tall Grass) they will drop as a resource. They cannot suffocate the player by falling onto them.

To obtain the dragon egg, the player may push it with a piston or place any non-solid block (like a torch) under the block the egg rests on and then destroy that block so the egg falls onto it. It is possible for the player to hit one while it is still moving to the point it breaks, however this is difficult. You may also use a sword while blocking to break the egg and get it that way, or, start to mine a block next to it with a pickaxe, and, while swinging the pickaxe (holding down the mouse button) aim for the egg, and it will start to mine it. It is also possible to obtain a dragon egg by using this command: /give @p minecraft:dragon_egg. You can also get it with TNT or some other explosion, but it won't always drop the egg.

The dragon egg will not burn in lava upon teleportation or falling.

Trivia

 * Ender Dragons destroy Dragon Eggs when passing through them.
 * 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 achievement The End. features a Dragon Egg as its icon. Its icon used to be a Monster Spawner block in the 1.9 pre-releases 3/4/5, due to the lack of Dragon Eggs at this time.
 * When hit with Flint and Steel, a Dragon Egg might break with one hit or teleport and appear in a new position, but still broken.
 * The dragon egg can be considered the rarest block obtainable in survival due to the fact that it only spawns once per world.
 * The dragon egg will fall into the Void if it teleports to a space where there are only air blocks between it and the Void.
 * The dragon egg's side sticks out into adjacent blocks, so if it falls into a one block space, the sides will clip through the blocks.
 * When a Dragon Egg is duplicated, the entity it drops will glitch and usually jump up to 3 blocks away.
 * When falling onto a Sign, a dragon egg will break and drop its item, like sand.
 * A Dragon Egg could theoretically be used as a lottery game, by mining out a room big enough for a numbered grid, and taking bets on which square it will teleport to next.
 * If a Dragon Egg goes through the End's End portal, it will appear at the original spawn coordinates in the Overworld. If it goes through the Overworld's End portal, it will appear on the obsidian platform.
 * The Dragon Egg uses a slightly altered Crying Obsidian texture (purple stripes instead of blue).
 * If the Dragon Egg falls onto a torch, it will break and fall as an item.