The most common problem with aircraft is simply failure of the plane to operate efficiently. Events such as engine failure, loss of fuel and decompression are the most common reasons an airplane crashes. Safety improvements in aircraft over the past hundred years have been implemented to mitigate these problems, however, it is almost impossible to prevent all failures.
Engine failure can come in the form of simple stalling or even involve the complete detachment of the motor itself. Designers have made improvements over the years to allow airplanes to fly if one or more engines fail. However, when a complete separation happens, the drag from the air can often be too much for even the most experienced pilot.
Other events such as metal fatigue also cause major problems. Over the course of time, the shell of the aircraft eventually loses strength due to the constant barrage of high velocities. Unfortunately, the phenomena was not fully understood until the late 1990s and design elements were not put in place prior to this time. Modern aircraft, however, are using multiple layers of materials, notably plastics, to prevent the damage caused by metal fatigue.