Sponge

Sponge is a block which currently has no uses rather than decoration. In the 1.8 update, Sponge will have new behavior and a variant, Wet Sponge.

Current (Pre-1.8)
Sponge can only be obtained in creative mode or by inventory editing.

Sponge rooms
Sponge can be obtained from 'sponge rooms' in ocean monuments.

Elder Guardians
Sponges are also dropped by elder guardians when they are killed by a player.

Pre-1.8
Sponges have no use but decoration.

1.8+
Sponges will absorb a 5x5x5 area of water around themselves in a 'sphere'. The sponge must be directly touching a water source to absorb water, and will only absorb water connected to an adjacent water block touching the sponge. They are useful for clearing large areas of water, although the finite amount of sponge in each ocean monument means that they need to be placed carefully. When a sponge absorbs water, it will convert to a wet sponge, which is darker, drips water, and is unable to soak up any more water. Wet sponges can be dried in a furnace. The most efficient way to use sponge is to start at the top and go down; sponges placed at the bottom will just result in water flooding the cleared area.

Drying
A wet sponge can be dried in a furnace making the sponge reusable. If a bucket is placed in the fuel slot after the fuel is used up, including if the fuel was lava in a bucket, the water will drain into the bucket. This is currently the only way to get the water back.