he Earth's protective atomsphere protects us from cosmic radiation - but in space the options are to provide shielding or take a gamble. Experts are unsure of how much radiation is safe, but at least this article mentions the possible shielding materials (handy for those who want to cover all cataclysmic possibilities on Earth):

The best option is where the shielding material also adds to the structural integrity of a ship as a whole. "When any material used as a radiation shield can serve a dual purpose, mission costs can usually be reduced," says Rapp. "For space radiation shields, materials with high hydrogen content generally have greater shielding effectiveness, but often do not possess qualities that lend themselves to the required structural integrity of the space vehicle or habitat." Rapp adds that graphite nano-fiber materials heavily impregnated with hydrogen may one day form the basis of future spacecraft shielding. But for now, radiation tests are predominantly conducted using aluminum or regolith shielding (virtually all of the lunar surface is comprised of regolith). ..."A 400-day round trip transit to and from Mars, and about 560 days on the surface... with 15 g/cm2 of aluminum shielding [would equal] about double the allowable annual dose for each leg of the trip to and from Mars." At the very least, Rapp says that at this time: "radiation effects and the effectiveness of shielding remain uncertain."

Source: ScienceAGoGo