String

String is an item primarily received by killing spiders and cave spiders, and used for the crafting recipes of many tools and utilities.

From spiders
Spiders and cave spiders drop up to 2 pieces of string upon death.

From cobwebs/tripwires
String can be obtained by destroying cobwebs and tripwires, which drop one piece per block destroyed.

From dungeons
String has an approximately 53% chance of spawning in a dungeon chest, where it will appear in stacks of 1–4 units.

From abandoned mine shafts
In abandoned mine shafts, there are cobwebs which can be cut with a sword or shears to get string.

From strongholds
Cobwebs can be found in libraries in strongholds, which can be used to obtain string.

As a crafting ingredient
String can be used to make wool, but this is rather wasteful as wool can be obtained from sheep; it is more economical to save string for making more fishing rods or more bows that can be used to make dispensers.

Tripwire
A tripwire is a small, gray wire that appears when string is placed. Tripwire is primarily used to output redstone signals when attached to tripwire hooks on opposite ends. Upon collision with most entities, a redstone pulse will be sent to the tripwire hooks connecting the tripwire. Tripwire's low visibility makes it an effective way of creating traps. Tripwire (along with tripwire hooks), generate only in jungle temples.

Usage
To activate a tripwire when it is connected, an entity (most mobs, minecarts, boats, arrows, items, etc.) must move on, through or over it. However, thrown potions, some arrows, thrown Ender pearls, and thrown eyes of Ender will not activate tripwire hooks. Destroying the tripwire while not holding shears will trigger a redstone pulse. The redstone signal must connect to the tripwire hook to be activated, not the tripwire itself. Tripwire can be connected to other tripwire for up to 40 blocks. You can connect hooks with tripwire on the ground or connect hooks through air (see details below). When a tripwire connection is formed, the hooks must be placed on both sides of the connection for it to have the ability to be activated.

Tripwires can also be used to help decorate a structure with vines. Placing a floating block of tripwire in midair without any attachments prevents vine blocks growing through it. This lets the player control where and how wide/long they want their vines to grow, or allows them to add patterns into the middle of large swaths of vines. This is particularly useful for high-altitude construction or floating islands that the player wants to have vines dangling from. Without a block to stop them, the vines will continue down until they hit the ground, but floating tripwires can keep them short and irregular without being seen for a more natural look (otherwise the player would have to use signs or other blocks that are conspicuous and/or bulky). This can also be used with carpets, as you can normally not place a carpet on Air, but you can on tripwire.

Placing and removing tripwires
Tripwires are placed with string. Tripwires connect like redstone wire, and can connect to tripwire on all four sides. Tripwire can be placed in the air, by placing it next to any solid block. Tripwire can also be placed on other tripwires. When breaking a block below tripwire, the tripwire is broken, activating the signal and string is dropped. If tripwire is placed on any block with transparency (glass, leaves, signs, air, chests, pistons, glowstone, slabs, stairs, etc.), it will not connect to tripwire hooks or tripwire placed on any block that is not glass or leaves. Yet, when one of these blocks is broken, the tripwire is not dropped nor activated (the tripwire remains in the air). This the same for when one is broken that has another tripwire placed on top. Tripwire has the same function when in the air as if it was on the ground. When making tripwires, Dinnerbone stated there either needs to be no blocks under any wire/hook or all blocks under the wire/hook; however this is not actually the case. Since this "mix and match" is based on whether or not the underlying block has a transparency value, any block with a transparency value can be "mixed and matched" with air. When breaking tripwire itself, it activates any tripwire or tripwire hooks that it was connected to. To disarm tripwire without activating the signal, you must break the block with shears. This will remove the block and drop string, yet will not activate the signal. Tripwire has the hitbox of a slab when it is not connected to tripwire hooks. When it is connected, the hitbox is the same as redstone wire, unless it's placed in the air. Tripwire can be "stacked" on itself when being placed, like stacking signs on signs, but it will still float after removing the tripwire/block under it.

Trivia

 * Walking onto or off from any piece of string next to a BUD switch, will cause it to update even if the string isn't connected to tripwire hooks. Breaking the block with Shears will do the same.
 * Tripwire has the highest resolution of any block in the game: 64x64. In 13w03a this is tied with the Locked Chest.
 * String is also referred to as "Silk".
 * Tripwire can be placed on top of itself.
 * When tripwire is placed upon ice or glass, its hit-box increases in size and the wire itself lays higher than normal. This makes it easier to see the wire, but it still functions as normal.