Everything was a race during the Cold War. From the '50s to the early '90s, communism and democracy duked it out in the Space Race, the Nuclear Arms Race, the propaganda race ... and, of course, the psychic-powers race.
Yes, psychic powers. Remote viewing (the practice of "seeing" distant locations using nothing but mind power) was a serious project carried out by serious people in the military and intelligence communities. There were programs looking into telepathy, cybernetics and other psychic phenomena, but the one that ultimately succeeded in raising some typically-cynical eyebrows was remote viewing [source: Szegedy-Maszak and Fenyvesi].
The CIA and the military conducted psychic experiments from the early '70s up until the mid-'90s, at a cost of $20 million [source: Szegedy-Maszak and Fenyvesi]. There was a big remote-viewing score in 1974 when a subject "saw" accurate details of the Soviet Semipalatinsk weapons site from a laboratory at Stanford University [source: Szegedy-Maszak and Fenyvesi]. But little came of it, and years later the CIA decided to scrap the whole project.
The U.S. government is no longer exploring the use of ESP for spying. As far as we know.