Difficulty

Difficulty can be toggled via the options menu in Minecraft. Changing this option has a direct impact in the gameplay itself. There are currently four difficulties in the game: Peaceful, Easy, Normal and Hard

When the difficulty is set to Peaceful, hostile mobs don't spawn naturally, with the exception of the Ender Dragon. When they spawn from spawners, they are removed from the game instantaneously. Players regain health over time. Despite regaining health over time, it is still possible to die if damage is received quickly enough. Switching from any other difficulty setting to Peaceful results in existing hostile mobs, except for hostile wolves and iron golems, being removed from the world. The Food Bar never depletes and players cannot eat anything except Golden Apples, unless the player has switched to Peaceful when their Food Bar was below the maximum.

Hostile mobs spawn in Easy difficulty. Enemies deal less damage than on Normal difficulty. Creepers will cancel their explosions after moving only a short distance away. The Food Bar can deplete and will leave the player with if it drains completely. Cave Spiders cannot poison players on Easy difficulty, and the Wither won't cause the Wither effect, although Wither Skeletons will.

On Normal difficulty, hostile mobs spawn. Enemies deal standard damage. The Food Bar can deplete and will leave the player with if it drains completely.

On Hard difficulty, hostile mobs also spawn. Enemies deal greater damage than on Normal difficulty. The Food Bar can deplete and will slowly kill the player if it drains completely. Creepers will not cancel their attack unless a large distance is between them and the player, making the explosion much harder to avoid. Zombies break through wooden doors. Spiders can spawn with potion effects.

Regional difficulty
Regional difficulty is the gradual increase of difficulty as players spend time in an area. This effect is capped and difficulty will not continue to grow after a chunk has contained players for more than 50 hours. Note that regional difficulty is a cumulative measure of time—if 50 players spend a single hour in a chunk, it will have maximum regional difficulty.

The effects of regional difficulty are limited to the mobs which naturally spawn in these chunks. If a mob is spawned due to lighting conditions, a spawn egg, or a naturally generated monster spawner, it will be affected by regional difficulty.

Moon phase
The phase of the moon has similar effects on the difficulty of naturally spawned mobs. The fuller the moon is, the higher the chance of naturally spawned mobs having various items and abilities and slimes are more likely to spawn aboveground in swamp biomes. Note that the moon does not actually have to be out for this effect to take place—the effect of the moon's phase exists even at daytime.

Hardcore gamemode
Hardcore causes the player to spawn in Hard difficulty and does not allow it to be changed. In single player, If the player dies, the world is deleted. In Multiplayer, If the player dies they are automatically banned from the server.

Trivia

 * Notch made a tweet on October 22nd 2010, stating that he's "changing difficulty to realism. Lowest setting = creative. Highest setting = starve". This was never implemented, however "hardcore" mode was added along with a creative gamemode.
 * Dinnerbone said in a Reddit AMA that you will have the option to lock any Difficulty