Obsidian

Obsidian is a deep purple and black block known for its high blast resistance and strength.

Obtaining
Obsidian is known as the sole block which can only be successfully mined with a diamond pickaxe.

Enchanting a pickaxe with "Efficiency" and using a beacon with Haste both drastically decrease the mining time. See the obsidian farming tutorial for more information.

Lava and water
Obsidian is formed when flowing water hits a lava source block, and can be found naturally where water from a spring or lake has flowed over a nearby lava pool.

Natural generation
Obsidian can be created when a Nether portal is spawned in the Nether or the overworld. This portal can then be mined, providing another way of obtaining obsidian renewably.

When a player enters the End, a platform of 25 obsidian blocks is generated for the player to spawn on. This platform can then be mined, and will be regenerated when the player reenters The End. Solid pillars of obsidian can also be found on the surface.

Obsidian also occurs naturally where underwater springs flow onto lava, often at layer 10.

As of 1.9, obsidian also generates as a part of end cities.

Ender chests
When an ender chest is mined with a pickaxe without the Silk Touch enchantment, it drops 8 obsidian.

Usage
Obsidian can be used to build explosion resistant structures. At 6,000, obsidian's explosion resistance is the highest you can obtain in Survival mode, other than anvils which have the same blast resistance. Obsidian cannot be pushed by pistons.

Nether portals
Obsidian can be used to create a nether portal frame, which can then be ignited using fire. The frame will be a vertical rectangle any size from 4×5 to 23×23. Note that the corners of the frame are not required.

Trivia

 * Obsidian is one of the hardest blocks to destroy in Minecraft. In reality, obsidian is glass-like in texture and quite fragile.
 * In real life, obsidian is an extrusive igneous rock like andesite, meaning that they are both formed from lava that has cooled down.
 * Destroying an obsidian block with a diamond pickaxe while underwater without standing on solid ground would take 3 minutes and 54 seconds. (Without the pickaxe, it takes 4 minutes and 10 seconds.) Either way, the player will run out of air long before the block is mined. (Unless a potion of water breathing is used)
 * It is a common misconception that enough TNT will destroy obsidian. Even though its explosion resistance rating is finite, additional TNT or other explosives will have no more effect on an individual block than only one (it would take 71.25 times the explosive power of TNT to destroy a block of obsidian). It is possible to hack or use an explosion strong enough to destroy obsidian, but no such explosion appears naturally.
 * The "Blue Wither Skull"'s ability to destroy obsidian is a special feature; its explosion is otherwise no stronger than a ghast's fireball.