Slimeball

The Slimeball is an item dropped by Slimes. Its only use is to make sticky pistons.

0-2 slimeballs drop when a Slime is killed. As slimeballs come from a mob, they are a renewable resource.

Player-invented uses
Previously, some multiplayer servers used slimeballs as tokens or cash due to the Slimeballs having no crafting purpose. However, since the 1.7 update, they are used in the construction of Sticky Pistons, making its currency usage undesirable. Further, players could simply get free slimeballs from Slimes if they were enabled in the server.

When in single-player, some players use them to show how many slimes they have killed.

In some adventure maps, slimeballs are used to keep score.

As a Crafting Ingredient
Slimeballs are used to craft sticky pistons. A demonstration video showing this.

Trivia

 * Before Beta 1.7, Slimeballs had absolutely no use.