The quote "Cowards die many times before their deaths: The valiant never taste of death but once" is found in William Shakespeare's play The Tragedy of Julius Caesar. The lines are spoken by Julius Caesar in Act 2, Scene 2, in response to his wife Calpurnia's fears about his impending death. 
Context:
In the play, Caesar's wife, Calpurnia, has had a terrible dream and pleads with him not to go to the Capitol. Caesar, trying to comfort her and dismiss the omens, delivers these lines to express his belief that death is inevitable and that one should not fear it. He argues that it is more painful to live a life filled with fear and hesitation than to face challenges with bravery, a concept he uses to explain the difference between a "coward" and a "valiant" person.