The Superman Curse is a superstitious belief that there is a curse over those who portray Superman in various media. This is based on a number of injuries sustained by such actors.
George Reeves was found dead in his Benedict Canyon home in 1959. The cause of death was a gunshot to the head. Authorities officially ruled it a suicide. However there controversy brewed over the years with talks of foul play. This is what started the belief in the curse.
Christopher Reeve, famous for portraying Superman in Superman: The Movie and subsequent films, broke his neck in a horseback riding accident. This was believed at first to be the result of the Superman Curse. However, he made the best of his misfortunes: he began a campaign for the advancement of medical technology and stem cell research.
As a result of such research, he slowly began to regain some functionality, and demonstrated the ability to move one of his fingers.
On on October 9, 2004 he went into cardiac arrest after receiving an antibiotic being used to treat an infection he had from a pressure ulcer that was causing sepsis earlier. He fell into a coma after that. Sadly on October 10, Christopher Reeve passed away at the age of 52. It is believed that an adverse reaction to the antibiotic was the cause of death.
Brandon Routh, upon accepting the role of Superman for Superman Returns, was asked in an interview if he was worried by the Superman Curse. He replied that it could be worse: he could NOT be cast as Superman and something terrible could happen to him.
Henry Cavill who portrays Superman in the 2013 film Man of Steel and the 2016 sequel Batman v Superman: Dawn of Justice states that he does not believe there is a curse, and that the incidents thought to be evidence are more along the lines of bad luck.