Obsidian

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

Natural generation
Solid obsidian pillars can be found on the End’s main island, generating all the way down to Y=0.

Obsidian also generates as a part of the end ship in end cities.

Obsidian also generates in woodland mansions with a diamond block concealed by it. These are found in the secret "obsidian room" and "lava room", on the 2nd or 3rd floors.

Obsidian also generates in sufficiently low underwater ravines and underwater caves.

In 1.16, obsidian generates as part of ruined portals.

Post-generation
Obsidian occurs naturally where underwater springs flow onto lava, often at layer 10 or lower.

Obsidian is created when a Nether portal is generated in the Nether or the Overworld. This portal can then be mined, providing a 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 gets regenerated when the player reenters the End. Obsidian pillars also regenerate when the ender dragon respawns.

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.

From block loot
Obsidian drops 1 obsidian when mined with a diamond pickaxe or netherite pickaxe. Otherwise, it drops nothing.

From bartering
Piglins may barter 1 obsidian when given a gold ingot with a chance of 9.43%

Info
Obsidian is useful for building explosion resistant structures, as along with anvils, it has a blast resistance of 1,200; the highest of all blocks obtainable in survival mode. Obsidian also cannot be pushed by pistons, and also cannot be destroyed by the ender dragon.

These qualities make obsidian an extremely effective defensive block, and it is commonly used in many bases in multiplayer servers as protection from griefers.

End crystals can be placed on top of obsidian, which can be useful in PvP combat, or just as decoration.

Breaking
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.

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

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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 runs out of air long before the block is mined (unless a potion of water breathing is used).
 * Destroying an obsidian block without a pickaxe, while underwater, without standing on solid ground, while under Mining Fatigue 3 from an Elder Guardian takes 50*5*5*5*370, or 2312500 seconds, or 26 days, 18 hours, 21 minutes, and 40 seconds. The derivation is from hardness times 5 (from not using a tool that can harvest the obsidian block) times 5 (from being underwater) times 5 (from not standing on solid ground) times 370 (from mining fatigue).
 * It is sometimes thought that enough TNT can destroy obsidian. Although though its explosion resistance rating is finite, additional TNT or other explosives has no additional effect on an obsidian block. It would otherwise take 71.25 times the explosive power of TNT to destroy a block of obsidian. It is, however, possible to an explosion strong enough to destroy obsidian.
 * The Blue Wither Skull has the ability to destroy obsidian as a special feature; its explosion is otherwise no stronger than a ghast's fireball.
 * In 1.16, obsidian will be one of four blocks that generates naturally in the Overworld, the Nether, and the End.
 * The other three blocks are air, bedrock, and chests.