The most common furnace problem is a dirty filter, which can restrict airflow and cause the furnace to work harder, leading to increased wear and tear and, potentially, a system shutdown. Regularly replacing or cleaning the air filter can prevent this issue and help maintain the efficiency and longevity of heating systems and air ducts. If the problem is not the filter, it could be related to the pilot light, thermostat, or electrical connections, all of which require professional diagnosis and service.