Rappelling, when you descend a rope by sliding down it using a specialized device, is the most dangerous part of climbing. Descending is one of the only times when your safety is based solely on your equipment.
Most of the accidents that come with rappelling are because of climber error. Some key factors to watch out for:
Knots at the end of the rope: Every year climbers fall to their death because they rappel off the end of their rope. This can be caused when the ends of the rope aren't even. Having a middle marker helps as does knowing the length of the rappel prior to heading down. Knots at the end of the rope will prevent the rope from going through your rappel device. Be careful!
Rig your rappel device correctly: This is another easy mistake to avoid. Double check and than triple check that all your carabiners are locked, that your harness is double backed, that the rope is threaded correctly.
Climbing accidents often occur when climbers are tired and when plans deviate from the norm. Use the buddy system and have your partner check your knots, your harness, and that the rigging is correct before descending. Make sure to be fully aware of what you are doing before you attempt any climbing endeavor. Proper instruction from a trained professional is a must.