Carpet

Carpets are thin blocks used for decoration. They are the same thickness as pressure plates. They are useful if you want a carpeted floor without using wool blocks as the material. They have a negligible hitbox, allowing a person to walk over them without elevating $1/16$ of a block. This is similar to how pressure plates work, although you cannot fall through a carpet. Carpets can be helpful when carpeting upstairs rooms without the ceiling of the next floor down being partially made of wool.

Crafting
Carpets are only 1/16 of a block and crafting carpets can be seen as wasteful, as if the carpets were crafted with maximum efficiency you would get 32 from the recipe.

Usage

 * Carpets must be placed on a block, and cannot be placed freely or be free-floating in the world.
 * Carpets can be pushed and pulled by pistons/sticky pistons, but will pop off if pushed onto a hole or pulled downwards.
 * You can craft Carpets by placing two blocks of wool of your desired color next to each other. This means that you do not need a crafting table to make them.
 * Carpets cannot be crafted with two differently colored wool blocks.
 * Carpets can break falling sand and gravel.
 * Carpets can be used as a safer alternative to decorative flooring. Note that while they were originally not flammable, as of snapshot 13w41b (1.7), they are indeed flammable.
 * Carpets are a more efficient alternative to flooring than full wool blocks.
 * Carpets do not prevent mobs from spawning.
 * Carpets placed above, or around, mushrooms growing naturally under trees will break the mushrooms if the mushroom is in a high light level, but will not break the carpet, leaving a floating carpet.
 * Carpets can be used to hide redstone wiring, pistons, hoppers, dispensers, and droppers.
 * Carpets can also be used to hide chests, thereby creating "hidden" storages.
 * Carpets can be placed on fences and walls allowing you to climb over them.
 * Carpets can be placed over water so that it can be walked on but still allow crops to be saturated and prevent items from falling into the water when crops are harvested. They will drop if the water beneath is removed, or if water (or lava) washes over them. Walking on carpet, placed on top of a water block also makes no footstep sound.
 * Carpets can be used to make mob proof passages. Just place a carpet on a sign with a hole of at least three blocks beneath it.
 * You can use any "non-full" block (such as tripwire, redstone, slabs, or other carpets) to achieve a floating carpet.
 * They can also be placed on Block 36, allowing for a true floating carpet (but since you cannot click on 36, it must be done indirectly).i

Trivia

 * Carpets will block the effects of book shelves when placed around an enchantment table, the same as snow cover does.
 * It is possible to use them to make a more realistic table by placing them on fence posts next to each other. However, you still can't put blocks on the table.
 * By putting carpet on a fence post, as mentioned above, one can then walk on top of the fence post by jumping, whereas normally one cannot jump on top of a fence post from the ground next to it. This is, because while the fence is normally counted as 1.5 blocks high and the player being only able to jump up about 1 block high, the carpet is counted as being just one block high, allowing you to jump onto it, then walk onto the fence (directly under it, however whose hitbox protrudes through the carpet) from the carpet. This also creates the illusion of flotation, however only by about half a block.
 * Carpets have a bottom texture.
 * When you place blocks on it, those appear a block above the carpet — like other partial blocks, carpets "claim" their entire block.
 * Unlike Pressure Plates, carpets cover the entire square they are placed on.
 * Carpet is an opaque block, however, it does not decrease light going through it.
 * This means undead mobs like zombies burn underneath it in the daylight.
 * This also allows hiding house lighting in the floor, rather than taking up wall, floor, or overhead space. Jack-o-lanterns are often used as a hidden light source, which would be much less appealing if out in the open.
 * If the player sprints across carpet, the particle effects are those of the blocks that are directly below it.
 * If the player puts a carpet on top of a bed and then sleeps in it, it will appear as if the player is underneath a blanket.
 * Carpet can be built on other carpet blocks, as well as pressure plates, beds and fences. If the block underneath the carpet block is removed, the carpet will be dropped.
 * If you place carpet next to a block such as wooden planks, if you walk on the very edge of the block, over the carpet, you will hear the wool footfall sound.
 * Carpets will retain qualities from some blocks they are placed on top of such as Ice (Slippery).
 * Carpets do not have their own texture, rather they borrow from the texture(s) of wool.
 * Carpets seem to not appear in your hand. They are in fact there, but they are too low down to appear on the screen.
 * In consequence, when in third person view, the carpet is noticeably detached from the player's hand.
 * Water blocks with carpet placed over them will still turn to ice in "Winter" biomes.
 * Mob AI's do not register carpet as a block they can walk on. This proves very useful in anti-mob passage ways. By placing the carpet above a block with no physical substance, like a sign, mobs don't register the carpet as something they can walk on, and provided a hole is underneath, the mobs will see just the hole and won't enter. This won't protect from a spider's jump attack, as it does not calculate height while doing this attack.
 * The same trick can be used for horse stables. By riding the horse onto the carpet, it thinks it's on a hole and won't move
 * Carpets can absorb a large amount of a creeper's explosive force.
 * Unlike wool, carpets are not destroyed quicker when using Shears.
 * In the Pocket Edition, only red wool can be crafted into carpets in Survival, which means that the only carpet color available in Survival is red. However, all colors are available in Creative.

Gallery
Teppich Tapis カーペット Carpet Dywan Ковёр 地毯