Radiation risk assessments based on exposures to the anticipated space ionizing radiation environment for a 180-day space station mission, 45-day and 90-day lunar missions, and 320-day and 600-day Mars missions are presented and discussed. Although lunar and Mars missions are also exposed to sporatic increases in the radiation environment from solar particle events, only risks for galactic cosmic rays (GCR) are considered here. In addition to the GCR environment, the space station will be exposed to trapped-belt radiation. Radiation-induced cancer mortality is taken as the end-point of concern. Risks are presented as functions of age and sex of the potential mission participants. Risks arising from exposure to GCR are less than 1 -percent for the space station, and lunar missions. To reduce the risk below 3-percent for a 320-day Mars mission, it will be necessary to select crew members of either sex that are at least 35-years of age. For a 600-day Mars mission, risks are greater than 3-percent for women of all ages. To reduce the risk to 3-percent for male crew members on a 600-day Mars mission, it will be necessary to select males of at least 45-years of age. Uncertainly of exposure estimates are discussed. Recommendations for future research are presented, including data on biological effects of heavy ions (especially as it applies to cancer mortality), and the investigation of other potential end-points such as effects of GCR heavy ions on the central nervous system. NASA-s commitment to the reduction of risks is presented and discussed. Additonal research needs to be conducted on the protection of astronauts from solar particle events.