In Answers To Gospel Questions Joseph Fielding Smith wrote: "... is doubtful that man will ever be permitted to make any instrument or ship to travel through space and visit the moon or any distant planet."

Following the Apollo moon landings and the death of President David O. McKay, President Smith became president of the Church. At a press conference following his assumption of Church leadership, he was asked by a reporter about this statement. President Smith replied:
"Well, I was wrong, wasn't I?"

http://en.fairmormon.org/Mormonism_and_science/Joseph_Fielding_Smith_claimed_that_man_would_never_walk_on_the_Moon