There's quite the story behind John Wayne's ownership of the island of Torcillo. He never paid a penny for it - it was gifted to him by the Government of Panama. Panama was in turmoil during the 1960s, Panamanian independence becoming a thorny political issue, and a crisis in the Panama Canal. Perhaps surprisingly, Wayne spoke out fiercely and repeatedly in support of Panama being given control of their own canal, and they were finally granted it in 1977.
Because of his support of Panama, Panamanian President Omar Torrijos decided the most appropriate way to thank Wayne was by giving him his own personal island in the shape of Torcillo. The island is sometimes also called Taborcillo, but most people in the area actually refer to it as 'John Wayne Island.' It now operates as a holiday resort, which includes a theme park.