Even if you don't get space sunburn from UV, the space environment would bombard astronauts with plenty of other types of harmful radiation, and they wouldn't have Earth's atmosphere and magnetic field to filter out most of the nasty particles. (Just to duplicate the protection that we normally get from the atmosphere, a spaceship would have to have metal walls that were 3 feet, or 1 meter, in thickness [source: Tate].)
A robotic probe sent on a flight to Mars revealed that astronauts making the same 253-day trip would be exposed to the equivalent of a whole-body CT scan every five or six days [source: Tate]. Scientists say that unless we figure out some better way to shield astronauts in interplanetary space, they would be at risk of dying along the way from radiation sickness. And even if they didn't, they would almost certainly succumb to cancer at some point [source: Halvorson].