Safety issues for future superconducting fusion magnet systems are examined. It is found that safety and failure experience with existing superconducting magnets is not very applicable to predictions as to the safety and reliability of fusion magnets. Such predictions will have to depend on analysis and judgement for many years to come, rather than on accumulated experience. A number of generic potential structural, thermal-hydraulic, and electrical safety problems are identified and analyzed. Prevention of quenches and non-uniform temperature distributions, if quenches should occur, is of great importance, since such events can trigger processes which lead to magnet damage or failure. Engineered safety features will be necessary for fusion magnets. Two of these, an energy dispersion system and external coil containment, appear capable of reducing the probability of coil disruption to very low levels. However, they do not prevent loss of function accidents which are of economic concern. Elaborate detector, temperature equalization, and energy removal systems will be required to minimize the chances of loss of function accidents.