Begining in the 1950s, the U.S. government began several avenues of research on the use of nuclear energy for various space applications. Programs suc as NERVA/Rover and Project Orion are examples of early research. Project Orion was eventually cancelled in 1965 due to the signing of the Test-Ban Treaty, since it involved using nuclear bombs to propel a spacecraft into orbit. NERVA/Rover were cancelled in 1972 due to political pressure after the sucessful Moon landing of the Apollo program after almost twenty years of sucessful research. NERVA/Rover projects were designed for Mars exploration and the development of a nuclear shuttle for use in supplying Moon bases, projects that were deemed to costly in the early 1970s. Project Timberwind was part of the Strategic Defense Intiative, and was cancelled before any ground testing could take place. Project Prometheus was a short-lived NASA and U.S. Navy project that would have developed fission power systems for powering  electrical propulsion systems. It was cancelled in 2005. Since then, there have been minor studies and research programs, but never a major, concerted effort to develop nuclear space systems.

Links to historical resources:

The Soviet Union/Russians have had several different research programs for both space nuclear fission and also nuclear thermal propulsion. Between 1967 and 1988 the former Soviet Union launched 31 low-powered fission reactors in Radar Ocean Reconnaissance Satellites (RORSATs) on Cosmos missions. The Soviet Union began developing nuclear thermal rockets in the 1950s also. When NERVA was cancelled in the United States in 1972, the Soviet Union scaled back their NTP program significantly. However, they went forward with ground testing. Around thirty successful ground tests of engines were conducted. With the collapse of the Soviet Union, much of this work ended.

Links to information on Soviet/Russion space nuclear systems