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.

Obtaining
The sponge currently only obtainable via Creative mode or inventory editing.

Future (1.8)
On June 8 2014, Jeb stated that he is re-adding sponges to survival for 1.8. They still clear water as they did before, though their mechanics are more complex than simply clearing a 5x5x5 area. They appear to remove source blocks only, not flowing water, in a 5x5 area, but if there is a barrier of some sort between the water the sponge is in and another pool of water (for example a solid block), the water in the other pool will not be absorbed. It will turn darker when it has absorbed water. The new sponges have undergone a slight retexture. The Sponge Block will be available in Survival Mode, but will not be crafted, and can be found by the methods below:

Obtaining
They can be found in Water Dungeons in a room in the Water Dungeon. The Elder Guardian, a boss mob that will be found in the same place, will drop sponge when killed by a player.

Smelting
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 the only current way to get the water back.