Mike Nichols, one of America’s most celebrated directors, whose long, protean résumé of critic- and crowd-pleasing work earned him adulation both on Broadway and in Hollywood, died on Wednesday. He was 83. His death was announced in a statement by the president of ABC News, James Goldston. 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...