"Can You Read My Mind" is the love theme from the 1978 film Superman (the day I bought my ticket, it was called Superman: The Movie), with music by John Williams and lyrics by Leslie Bricusse.
The music is a theme for Lois Lane, played in Superman by Margot Kidder. It was originally recorded as a pop-influenced piece, but as that original version would have dated the picture, a more orchestrated and timeless version was done for the final film.
It has been said that either Karen Carpenter (The Carpenters) or Toni Tennille (Captain and Tennille) were originally considered to perform the vocal, but there is no existing proof that either one actually did it. What is known is that the producers of Superman tried to get Margot Kidder herself to actually sing it, but, according to Richard Donner's commentary track for the Superman DVD, "it didn't sound right." So it was decided that Kidder would just recite the lyrics, and this vocal track is what was used for the final film version.
Shortly after the film's release, Maureen McGovern recorded the song proper for the hit single version, which incidentally did not appear in the film.
And why not, here's the opening credits sequence to Superman: The Movie (it does include the "love theme"):