Catastrophic falls are one of the leading causes of injury and death in the outdoors, however many are quite preventable. Here are a few general safety tips for hiking in steep terrain.
*Ankle support. When hiking in steep terrain, use boots not shoes. There are plenty of "lightweight mids" that will fell like sneakers on your feet, but still support an ankle fatigued from hiking. You can even trail run in them.
*Soles. The more rocky and steep the hike, the more you should consider getting footwear with some good, sticky soles. Vibram soles are recognized by climbers, hikers, and soldiers alike for their durability and grip. They are also known for still being able to maintain traction when the stone/rock you are stepping on is wet.
*Do not go beyond barriers for better views or pictures. In Yosemite National Park and the Grand Canyon both, this is commonly how people accidentally go over cliffs and waterfalls. Follow the instructions on sinage.
*Stay away from the edge. These steep banks and cliffs are formed by erosion. Banks can be "undercut" and you never know how stable an edge is.
*Crawl, don't climb. Rock "scrambles" are one thing, but never "ladder style" climb hillsides/cliffs/outcroppings with proper equipment and training. You can scramble down, but vertical pitches are nearly impossible to down climb without falling. The experience and weight distribution is completely different than up climbing.
*Remember to always let someone know your route, and when to expect your return when exploring the outdoors. The sooner the rescue is started the better, as you may be too incapacitated to call for yourself.
*Always carry a proper first aid kit on the trail.