People asked the Coast Guard to help the people stranded on Gilligan's Island. They thought the show was real!
Gilligan's Island, perhaps one of the most well known sitcoms to come out of the 60's is about a bunch of people that become stranded on a deserted island and they try to survive. To most viewers of the show, it was a humorous sitcom that was extremely entertaining. However, to certain viewers, they thought the show wasn't scripted and that people were actually stranded on a deserted island and trying to survive.
It wasn't uncommon for the Coast Guard to recieve telegrams from different people urging them to sail out to Gilligan's Island and rescue the poor people that were stranded there! The Coast Guard simply forwarded the messages to producer Sherwood Schwartz, most likely after laughing for a few minutes.
<a data-cke-saved-href="http://en.wikipedia.org/wiki/Gilligan" href="http://en.wikipedia.org/wiki/Gilligan" s_island#production'="" target="_new">(Source)