String

String is an item primarily received by killing Spiders or Cave Spiders, which drop 0 - 2 strings on death, but can also be obtained by destroying Cobwebs and Tripwires, which drop only one piece. String has an approximately 53% chance of spawning in a Dungeon chest, where it will appear in stacks of 1 - 4 units. This is not a practical way to find String though, since killing spiders can be used to get string more quickly and in larger amounts. In Abandoned Mine Shafts and libraries in Strongholds there are Cobwebs which can be cut with a sword or shears to get string. Tripwire (along with Tripwire Hooks), generate in Jungle Temples, which can be punched for collection, but also sheared and not activate any redstone.

Crafting
String is a vital component to two recipes, the Bow and the Fishing Rod. String can also 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.

String can be placed on the ground as a Tripwire. Hooking them up to Tripwire Hooks will allow redstone current to be activated by mining or walking over the string. It is difficult to see the string, making it useful in traps.

String can also be obtained by cutting Cobwebs and Tripwires. Cobwebs are mostly found in abandoned mineshafts, but also in stronghold libraries. Tripwires are found naturally currently only in jungle temples.

Use as Tripwire
A Tripwire is a small, gray wire that is placed with String. Tripwire can output a redstone signal when walked over if configured correctly.

Usage
Tripwire can be activated to output a redstone signal, yet it must be attached to two Tripwire Hooks on each side to output the signal. Tripwire can be connected to other Tripwire for up to 40 blocks.Tripwire does not require a block under it to work. 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. To activate a Tripwire when it is connected, an entity (mobs, minecarts, boats, arrows, items, etc.) must move on, through or over it. The redstone signal must connect to the Tripwire Hook to be activated, not the Tripwire itself.

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).

Placing and removing Tripwires
Tripwires are placed with String. The actual Tripwire block can only be obtained through inventory editors or /give. This item can be placed like normal String can be placed. Tripwires connect like Redstone wire, and can connect to Tripwire on all four sides. Tripwire can be placed in the air, by placing it on top of 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(Grass, 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 weather 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.

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.