Apple

Apples are food items that can be eaten by the player.

From trees
Oak and dark oak leaves have 0.5% ($1/200$) chance of dropping an apple. This amounts to approximately 25% chance to get an apple from an oak tree and 60% chance from a dark oak tree.

From loot chests
Apples can be found in chests found in strongholds and villages, as well as in the bonus chest.

From trading
Villager farmers may offer to sell apples in exchange for emeralds. 5 apples can be bought per emerald as one of their third tier trades.

From Notch
Killing Notch in multiplayer will drop an apple in addition to his inventory.
 * Note: This no longer works since at least Beta 1.7.3.

Usage
Eating an apple restores and 2.4 points of saturation.

As a crafting ingredient
An apple can be used to craft a golden apple or an enchanted golden apple.

Video
Note: The video shows golden apples being crafted with gold nuggets. This is outdated, they are now crafted with ingots (with the exception of the Xbox 360 Edition, which still uses nuggets).

Trivia

 * The sprite of red apples was the same as used in Notch's game Legend of the Chambered.
 * In Pocket Edition there is a higher chance of getting apples from decaying leaves.