Cobweb

The cobweb is a block introduced in Beta 1.5. It was previously found in the terrain.png file, but had no block ID assigned to it. It cannot currently be crafted.

They were added in Beta 1.8 and are generated in Abandoned Mine Shafts. Near the cave spider spawners, they are created in large amounts. They also generate in Strongholds, especially in the libraries.

Moving into a cobweb limits your movement abilities. When you are "inside" the cobweb, you will move at a speed equal to about 15% of the normal walking speed. Additionally, jumping will vibrate the player, akin to jumping in a 2 block high space. Dropping an item into it will make the item stick and gradually sink through it. Unlike water, however, falling into a cobweb will not prevent fall damage, although it will be delayed until you make contact with the ground.

When cobweb is destroyed by shears, pistons, running water, or a sword, it drops 1 string. Cobwebs are also flammable, but they can't be ignited.

As of Beta 1.8, cobweb can only be placed in creative mode, as it turns into string when harvested and cannot be crafted.

History
Notch originally planned for spiders to produce webs.

Slowing effect
Actually, the slowest you could go is not moving at all. -Podote I agree with you Podote.
 * Items thrown on the cobweb are also slowed and will fall down after about 20 seconds.
 * A block of Sand or Gravel which falls or is shot into a cobweb, will slow down, then be destroyed and become a resource after about 4 seconds. Primed TNT seems to be not affected by this phenomenon, as it doesn't disappear and will eventually explode; destroying the cobweb.
 * Mobs that walk into the cobweb will slow down, excluding spiders and cave spiders.
 * Players are unaffected by cobwebs when in a minecart, except when they are in the way of the cart. This allows creation of a mob-slowing tunnel that can be ridden through with ease, making safe rooms even safer.
 * A shot Arrow will pass through cobwebs without being slowed down.
 * Placing cobwebs on Ice will increase the slowing effect of the cobweb.
 * Cobwebs will slow the time of a player breaking blocks like when in water.
 * It takes exactly 8 seconds to get across a cobweb on top of Soul Sand with ice under, given that you had a running start and did not jump.
 * The slowest you can go in Minecraft is by placing a cobweb on soul sand, then placing ice under the soul sand, and finally, walking through it with Sneak Mode (left shift) activated, and blocking with the sword after throwing a potion of slowness at the ground.

Fall damage

 * Jumping from as little as one block above a cobweb, onto it, will induce half of a heart in fall damage.
 * When falling into a cobweb, if a player gets into a minecart or boat before hitting the ground, they will not take the fall damage until they exit the cart/boat.
 * When falling from a height that would normally kill you, landing in a cobweb will delay the damage until you touch another block.

Trivia

 * Cobweb blocks can be used as air pockets in the same manner as Sugar Cane.
 * Cobwebs can be placed on any block, including transparent blocks or even other cobwebs.
 * Signs and Paintings can be placed on cobwebs.
 * Ghasts will not see players in or behind cobwebs.
 * No kind of mechanism (excluding Dispensers and Note Blocks) can be placed on top of cobwebs.
 * In SMP, the particles given off when breaking a cobweb may slow down whilst falling, as they appear before the cobweb block disappears. This also seems to cause them not to fly outwards, but just drop directly downwards after the cobweb disappears. This phenomenon only seems to happen if there is a considerable amount of lag on the server.
 * Destroying a cobweb makes "Stone" sounds.
 * While traveling down through a cobweb and attacking, it counts towards critical hits the same as jumping while attacking would - even if you did not jump into the cobweb.
 * As Mineshafts have cobwebs inside them in sparse amounts, finding a room inside the Mineshaft almost completely full of cobwebs indicates that the room contains a Cave Spider spawner.
 * It is incredibly difficult to fight Mobs in cobwebs.