Bunny Link

In A Link to the Past, Link transforms into, a fluffy pink rabbit, upon entering the Dark World. This is because the Dark World changes people to reflect their true nature. Although it is never mentioned, Link may have become a bunny because he has the timid compassion and kindness of a rabbit. In this form, Link is completely defenseless and cannot use any of his weapons. He can retain his original form after obtaining the Moon Pearl from the Tower of Hera.

In other parts of his adventure, he can be transformed into a rabbit by coming in contact with rotating, golden, star-shaped objects. However, this change wears off after a few seconds or after being hit by an enemy.

Theory
Some people believe that this transformation has some correlation to Wolf Link from Twilight Princess. They believe that Link is transformed into a wolf because a wolf accurately reflects Link's heart. More accurately, the chosen hero who has been selected by the Gods will transform into a divine beast upon entering the Twilight Realm. This legend was told to Link by Midna, who knew upon first seeing him that he must be the divine beast chosen to save her world.