They said that the western world see the man in the moon, but in the eastern world they see a rabbit in the moon. Stories on how this begin go back thousand of years ago. There're many legends about the rabbit in the moon but the most common one goes something like this.
A rabbit, monkey, fox and otter were friends. One day the Buddha came along disguised himself as a hermit begging for alms. The otter took off into the water and brought the hermit some fish. The fox was able to find some milk-curd to give to the hermit. While the monkey climbed a tree and retrieved some fruit and gave it to hermit.
Unfortunately, the rabbit had nothing to give except some grass which the hermit could not eat, so he threw himself in the fire to become a meal for alms beggar. Immediately the Buddha revealed himself and saved the rabbit from the flames. He then rewarded the rabbit by drawing his picture in the moon.
The truth is I've never seen one, maybe because I always see the moon like this