Moon

The Moon is a sprite that appears during night time.

Grass blocks or Saplings do not grow in moonlight unless there is a Torch (regular or Redstone) or other light source nearby, however they won't decay in moonlight either.

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.

Mobs
Hostile Mobs will spawn around dark areas of a normally generated map. When the moon is up, hostile Skeleton, Creeper, Zombie and Spider mobs will appear and attack the player. When the sun comes back up Skeletons 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. 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 rotate as the night progresses.

Future
As of 1.8, the night-time will be illuminated to level 4 with a cooler blueish tinge, rather than the current lighting color. Thus making it more like moonlight.

Trivia

 * Night time lasts 7 minutes, plus 1.5 minutes each of sunrising and sunsetting.
 * You can't see the Moon or Sun while using the short or tiny render distance settings.
 * The moon is 8 x 8 pixels.
 * The stars are randomly generated using a seed, but that seed is always the same, and thus the stars are always generated the same way.
 * The Sun and Moon seem to appear larger when in the corner of the Minecraft window.
 * In the past there was a stars file in the jar, but at some point it was replaced with the randomly generated stars.
 * Along with the sun, the moon was said by Notch to rise in the north in a twitter post.

Mond Lune Księżyc Луна