It's about as safe or as dangerous as you want it to be. While there is always some inherent danger in the sport, most problems are due to "pilot error". Pay attention to posted signs... they're there for a reason. Ride in control. Don't ride in closed areas.
The injury rate for skiing has been fairly level at about 3 injuries per thousand skier-days. These injuries include everything from minor bruises and lacerations to broken necks. The most common injuries are thumb and knee injuries. Snowboarders experience about the same injury rate as skiers but the injuries tend to be to the wrist, ankle, and neck (refer to the injury section of this FAQ (1.11) for more info).
You can kill yourself snowboarding. Even worse, you can also kill
somebody else. Stay in control. Don't go out of bounds without knowing
what you are doing, knowing the risks and taking responsibility.