Mycelium

Mycelium is a block similar to grass blocks, but it is only found natively in Mushroom Biomes. It can grow over dirt blocks that are in proximity in a similar way to grass.

Behavior
Mycelium looks and acts very similar to grass. One of its defining characteristics is that the tops of Mycelium blocks have a particle effect that resembles tiny spores being released constantly from the surface. This effect persists even when the Mycelium block is covered in snow; the sides will use the same texture as snow-covered grass, with the spores being the only way to visually tell them apart.

Mushrooms spread faster on Mycelium than on other blocks, and Mycelium is the only block on which mushrooms can stay when an adjacent block is updated despite a light level that is normally too high for the mushroom to remain. It is also one of three blocks, along with dirt and grass, on which Huge Mushrooms may grow.

Like most other blocks, both hostile and friendly mobs may spawn on it under the right conditions. Saplings and flowers cannot be placed on Mycelium, and it cannot be tilled with a hoe to make farmland.

Otherwise, it behaves identically to grass. When harvested, Mycelium normally yields a dirt block, but the Silk Touch enchantment can be used to acquire a Mycelium block. In Creative Mode, it can be equipped and placed like any other block.

It's the only block on which mushrooms can be planted and spawned while in direct sunlight.

Spread
Mycelium is only found naturally in Mushroom Island biomes, but it can spread anywhere or be pushed anywhere with a piston.

Mycelium spreads in exactly the same way as grass: A mycelium block can spread to any dirt block within one space above, one sideways, or three down. The mycelium needs light level 9+ above it and the dirt needs light level 4+ above it, and must not be covered by any light-impeding block i.e. water, ice, lava, slabs, stairs, farmland, or any opaque block. Mycelium also dies under the same conditions as grass: when covered by one of the light-impeding blocks above and the light level at that block is below 4.

Mycelium and grass do not replace one another; whichever arrives on the dirt first will remain. If there is a sapling or flower on a block of dirt when mycelium spreads to it, the plant will pop out and drop as an item.

Generated caves and ravines in a Mushroom Island biome will not remove mycelium, often leaving a thin layer over a ravine or 'bars' of mycelium covering a cave.

Bugs

 * If a layer of snow is on top of a Mycelium block, it will use the snow covered grass texture instead of one unique to Mycelium.

Trivia

 * It is a common misconception that only mooshrooms can spawn on mycelium. This is not true; friendly and hostile mobs can spawn on mycelium just as on any other block. It is the mechanics of the mushroom biome that prevents other mobs from spawning. Relatedly, mycelium outside of a mushroom biome will not spawn mooshrooms.
 * The spore particle effect is called "townaura" in the game code. This may indicate that the gray particle effect was originally planned to mark the area of villages, along with the unused textures in terrain.png.
 * Notch has already mentioned that villages may receive their own biome.