Golden Apple

Golden Apples are a food item. They are moderately difficult to obtain, but are the most beneficial food item. They are extremely rarely found in dungeon and stronghold chests, though they can also be obtained by crafting a Red Apple and eight Gold Nuggets together. Eating one not only restores, but grants "enhanced regeneration" for 5 seconds, healing up to health over that time. They can be eaten for the regeneration even if you are full. When fed to Zombie Villagers under the effects of a Potion of Weakness, they will eventually be cured.

Enchanted Golden Apples are far rarer and more powerful, even more powerful than the original. Enchanted Golden Apples shine purple, much like enchanted tools and armor. These cannot be used to cure Zombie Villagers. The Enchanted Golden Apple requires an apple and 8 Gold Blocks, 81x more gold than a standard Golden Apple.

Crafting
Normal Golden Apple. In the Xbox edition, it uses Ingots instead of Nuggets. It has the same effects however: Enchanted Golden Apple:

Advantages

 * They are the only food items that cause temporary constant health regeneration that is not dependent on the player's hunger. This is indicated by the line of hearts bobbing up and down in a wave pattern, with each full wave restoring half a heart.
 * Compared with potions of regeneration, golden apples are available for fighting monsters before the player is able to brew or even go to the Nether in single player mode. (Brewing requires Blaze Rods and Nether Wart, both found only in the Nether.)  In particular, the enchanted version provides Fire Resistance, which is handy for collecting one's first few Blaze Rods.
 * Golden apples also are stackable up to 64 (like other food), whereas potions take up an inventory space for each potion.
 * Golden apples are the only food that can be eaten when the player has a full hunger meter.
 * Although red apples have a low chance of dropping from oak leaves (0.5% per leaf block), tree farming can produce a good supply of them.
 * Golden apples are technically renewable, but see below.
 * Golden apples can be used to create a village by curing zombie villagers. If Generated Structures are turned off, this is the only way to have villagers and trade with them.

Disadvantages

 * Golden apples have an extremely slim chance of appearing in dungeon chests: 0.7%.
 * Golden apples are technically renewable (for advanced players), because the gold they require can be "harvested" by attacking Zombie Pigmen. In practice, they will require mined (non-renewable) gold.  There are 9 gold nuggets in one gold ingot, and 9 ingots in one block of gold.  Therefore, it will take most of one ingot to make a normal golden apple, but it will take 72 ingots (648 nuggets) to make an enchanted one.

Trivia

 * Due to this item being able to heal the player a large amount, they are commonly found as rewards in custom adventure maps.
 * Enchanted Golden Apples provide the highest level potion effect thus far: Regeneration IV. The healing speed is enough to outrace nearly any source of damage short of explosions.