Shears

Shears are a tool used to obtain wool from sheep and harvest placeable leaf blocks by right and left-clicking, respectively.

Uses
Shears are the most efficient way to acquire wool from sheep (each yielding 2 - 4 blocks when sheared). Punching a sheep will not cause any wool to drop, and killing it will only yield a single block of wool. Sheep can be painted with dye before shearing to efficiently produce colored wool.

Many players would use leaf blocks to create good-looking hedges for gardens, etc. With the introduction of shears, they can now legitimately obtain placeable leaf blocks in-game.

Shears can also be used to destroy cobwebs in half a second to yield a piece of string.

History
In Beta 1.7, shears were introduced into the game. They were first mentioned by Jeb on Twitter The tweet revealing Jeb's work on shears was written in Swedish pirate language (Jag jobbar på shears nu) which translated to "I'm working on shears now". Shears were originally planned as a way to defuse TNT, but Jeb dropped this shortly after deciding TNT would only detonate with redstone or fire.

Before Beta 1.7, sheep would drop 3 wool blocks at most when hit, but shears can harvest up to 4 wool blocks per sheep. This incentive is part of an upcoming plan to have animals stay in the game longer, like allowing sheep to regrow wool (and therefore, shearing as opposed to punching as a collection method for it).

Trivia

 * Shear and Hoes are the only tools to have a specific right-click action. Also, Shears are the only tool that has a specific right-click action (shearing sheep) and left-click action (collecting leaves).
 * Hitting a wool block with shears will break it quickly, but not damage the shears themselves.