1938's War of the Worlds

From National Geographic:

It was the day before Halloween, October 30, 1938. Henry Brylawski was on his way to pick up his girlfriend at her Adams Morgan apartment in Washington, D.C. As he turned on his car radio, the 25-year-old law student heard some startling news. A huge meteorite had smashed into a New Jersey farm. New York was under attack by Martians. "I knew it was a hoax," said Brylawski, now 92. Others were not so sure. When he reached the apartment, Brylawski found his girlfriend's sister, who was living there, "quaking in her boots," as he puts it. "She thought the news was real," he said.

As we learned in The Adventures of Buckaroo Banzai Across the Eighth Dimension, the invasion at Grover's Mill, N.J. was real and the radio show was a coverup. More on War of the Worlds here.