Moon

The Moon is a sprite that appears during night time.

The moon illuminates topmost blocks during the night in the same way that the sun illuminates them in the day, but only illuminates them to a Light level of four, rather than the sun's fifteen.

Grass blocks or Saplings do not grow in moonlight, however they won't decay in moonlight either.

Phases of the Moon
The Moon goes through eight lunar phases. The phases are (in chronological order): This would allow the player to keep track of the passage of time via the Lunar calendar. A full cycle of all eight phases is equal to one Lunar month or Lunation. Thirteen and 1/2 lunations is about equal to one lunar year.
 * Full Moon
 * Waning Gibbous
 * Last Quarter
 * Waning Crescent
 * New Moon
 * Waxing Crescent
 * First Quarter
 * Waxing Gibbous

Mobs
Hostile Mobs will spawn around dark areas of a normally generated map. When the moon is up, hostile Skeleton, Creeper, Zombie, Endermen and Spider mobs will appear and attack the player. When the sun comes back up Skeleton and Zombies will burn in the sunlight and drop items after death. Spiders will not burn in daylight, but instead become neutral during the day, only to become hostile again if attacked, when it is night, or when it falls into a dark area. Endermen will not burn in daylight, but instead become neutral during the day, only to become hostile again if attacked or looked upon, but will instantly teleport away and become neutral again if the Player approaches them. Creeper and Slime mobs do not burn, and will remain hostile during the day (See also: Difficulty level)

Stars
Together with the moon, the night sky also consists of stars. The stars look like little white squares and are an overlay over the Void that rotates as the night progresses.

Trivia

 * Night time lasts 7 minutes, plus 1.5 minutes each of sunrising and sunsetting.
 * The Moon and Sun are not visible while using the Short or Tiny render distance settings.
 * According to Notch, the Minecraft sun and moon actually rose in the north, not in the east. This was a bug, but was left in the game. This was changed in Beta 1.9 Pre-release 4, so the sun and moon now rise in the east.
 * In Beta 1.9 Pre-Release 4, one can find out on which hemisphere his/hers Minecraft world is by studying the moon phases (see gallery). The hemisphere that the world is on seems to be chosen randomly and stays the same, no matter how far the player goes.
 * The Minecraft Moon is rotated 90 degrees. It appears to be lit from a source in the north or south, whereas it should be lit from the east or west.
 * The Minecraft Moon is fixed in the Sky relative to the sun and stars. Earth's Sun and Moon move more slowly against the stars, and the Moon moves more slowly than the sun.
 * Minecraft cannot have eclipses due to the above.
 * The Minecraft Moon can only be seen at night (unlike the real Moon), unless you are past the building height limit.
 * If a player is viewing themselves from the front in third person, during moonrise, the moon will appear red.