Dryly urbane, Mr. Nichols had a gift for communicating with actors and a keen comic timing, which he honed early in his career as half of the popular sketch-comedy team Nichols and May. He accomplished what Orson Welles and Elia Kazan, but few if any other directors have: He achieved popular and artistic success in both theater and film. He was among the most decorated people in the history of show business, one of only a handful to have won an Oscar, a Tony, an Emmy and a Grammy.