Clay

Clay is a block that is a light-blue/gray recolor of the Sand texture.

Clay can be found on the surface in groups of varying number usually surrounded by Sand. Despite common belief, clay's spawning is not tied to water and sand, but just to sand, and can spawn in the middle of deserts. It is usually exposed, but is sometimes found under sand or water. It is uncommon, but is easier to find than other "rare" blocks (like Gold) due to the fact that one only needs to explore surface-level deserts or beaches to find it. Clay was a lot less common before the Halloween Update.

It can be mined with any type of tool, but Shovels are the optimal choice. Destroying clay blocks will yield 4 balls of Clay each, which can be crafted back into a clay block or smelted into brick.

By hitting F5 you can enter third person mode. In third person mode you can adjust the camera angle to easily see underwater. This is very useful for efficiently looking for clay blocks from a boat.

If you're having trouble seeing if a block is clay or not, look for the characteristic lines of stone. Clay is usually a lighter color than stone and appears to be smoother. Clay also sounds like dirt and mines much faster than stone (especially with a shovel).

Trivia

 * In real life, Clay can actually be bright red, not just gray.
 * Clay can also be found a few meters under the soil in real life.
 * Clay is actually rarer than Diamond, but it is easier to find, as it is always generated on the surface, while diamonds are usually surrounded by Stone.
 * Clay can be easily found in the middle of an expanse of water. When sand is on the surface or a block under, there is a chance that clay is there, too. Use a boat to find these areas.
 * If inventory space is tight, clay balls can be formed back into clay blocks using the 2x2 inventory crafting grid. As blocks, clay can take up to 4 times less space, but in order to revert the clay blocks back into balls for smelting into bricks the clay blocks must be placed and destroyed again.
 * As of beta 1.6, in newly generated chunks clay blocks are nearly nonexistent. To be specific, clay only generates when the x and z coordinates are the same, severely limiting the amount of clay on the map.
 * Notch discusses the above statement on reddit with many comments. http://www.reddit.com/r/Minecraft/comments/hof4w/clay_formula_in_166_xz/c1x19y1?context=3