According to one legend, Brahma had a beautiful daughter but he was overcome by lust for her. She escaped by taking the form of a deer. Brahma adopted the form of a stag to chase her into submission. However, Lord Shiva prevented any unlawful action by firing an arrow at Brahma which wounded him. Ever since then he appears in the heavens as a deer-shaped constellation of stars ( Mrigasirasam ) with Shiva's arrow speeding after him.
Lord Shiva took the form of a deer while in the forest Shleshmantak in Nepal. There is a shrine to his consort Parvati, as Vatsyaleshvari, who encounters a divine deer. Shiva is also frequently depicted holding a deer in his hand or wearing deer skin indicating the Yogi's mastery over the mind.
Some even consider the deer to be the vahana of Lord Vayu, the Hindu wind-God.
(Legend source: www. khandro .net )
The deer is considered sacred by the Buddhists as well. It is believed to be the perfect messengers of the sacredness of life because of its graciousness, gentleness and dignity. It was in a deer park that Buddha preached his first sermon. In Buddhism, there is a mandara (sacred drawing) which depicts a deer standing on a white cloud with the Tree of Life above its head. Because the deer is considered the messenger of universal love, meditating upon this mandara is said to open one's consciousness to the mystery of infinite peace.