Boy Saves A Baby Fawn, Bangladesh

Saint Hubertus saw a stag with a crucifix between its antlers while hunting on Good Friday and was converted to Christianity by the vision. This story was transferred to Hubert from St Eustace, of whom it was originally told.
In The Lion, the Witch and the Wardrobe, the first book in The Chronicles of Narnia series, the adult Pevensies, now kings and queens of Narnia, chase the White Stag on a hunt, as the Stag is said to grant its captor a wish. The hunt is key in returning the Pevensies to their home in England.
In the Harry Potter series, the Patronus Charm that Harry Potter conjures to repel Dementors is a silver stag. James Potter, Harry's father, had an Animagus form as a stag. Also, Harry's mother Lily Potter, and subsequently Severus Snape's, Patronus form was a doe.
In one of the stories of Baron Münchhausen, the baron encounters a stag while eating cherries and without ammunition, fires the cherry-pits at the stag with his musket, but it escapes. The next year, the baron encounters a stag with a cherry tree growing from its head; presumably this is the animal he had shot at the previous year.