Chances of the elevator falling are extremely rare as any one of the many required cables can individually hold a fully loaded elevator in place. Even under the horrifying conditions of the World Trade Center bombing, hundreds trapped in elevators were rescued by elevator industry specialists and firemen, many in minutes. Use the alarm button or stay on the phone if there is one, stay calm and most importantly stay inside. When help arrives, follow instructions for a safe exit. In case of fire, never use the elevator, use the stairs.
Building codes require exit stairwells to provide a good measure of protection in case of fire.
Stairwell doors are heavy and usually totally enclosed and well lighted and designed to protect people from smoke and fire. In addition, on stairs you control the option of going up or down to avoid the fire and smoke. Elevator shafts are often not sealed and act as a chimney thereby attracting the smoke. Most modern elevators are programmed to automatically return to the ground floor when the alarm is triggered. They will shut down and remain available for fire fighters only, so they won't respond to calls.