Cobweb

The cobweb is a new item 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're created in large amounts. They also spawn 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

 * 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 10 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.

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 will kill you if you land in the cobweb it won't kill you, but as soon as you exit the cobweb and touch a different block you will die.

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.
 * Whilst traveling down through a cobweb and attacking, it counts towards critical hits the same as jumping whilst attacking would - even if you did not jump into the cobweb.
 * Cobwebs have proven to be useful particularly in water-filled moats 3 blocks in depth. Adding a layer of cobweb to the bottom of the moat will render any mob (or players) stuck. It is possible to get out (granted you will lose health from a near drowning experience) but most mobs will drown. This is a particularly efficient method of repelling creepers from hiding around the corner of your house entrance.
 * Additionally, creating a tunnel under the moat can be used to safely collect anything the dead mobs drop. After the mob drowns, whatever they drop will sink through the cobwebs.  The cobwebs "ceiling" will keep the water from filling a tunnel under the moat and you will be able to collect the drops.