Air

Air is an invisible non-solid Block that is meant to represent the absence of a block. Although technically a block, it is usually not seen as such. Air can only be destroyed or created by the placement or removal of other blocks. Air and other non-solid blocks are the only spaces the player and other Mobs are allowed to move within.

When coming out of the water, air will restore all bubbles on the players' air meter and make it disappear. Entering an opaque block will suffocate whatever is inside, while air will stop the suffocation.

History
In the Indev versions, air affected fluid blocks that were horizontally adjacent to it. If air was touching the fluid block, there was a 2/3 chance the Fluid block would disappear and make the pool recede and a 1/3 chance the fluid block fill the air, making the pool spread.

Clouds
There are two types of clouds: 2-dimensional and 3-dimensional. Pre-indev releases had 2-dimensional clouds, while post-infdev releases have 3-dimensional clouds (with the ability to turn them into 2-dimensional versions via the "fast/fancy" option).

Trivia

 * Giving yourself air blocks by means of the /give or /item command will cause Minecraft to crash.
 * In your Inventory, air has Fire's icon, and its labeled as "Undefined Item".