Ive seen motors completely fail due to excessive dirt buildup on and around the motor, or ignitors short out because of dust or lint buildup on the surface. Imagine having to fork out two, three, four hundred dollars or more to replace a failed part simply because routine maintenance has not been performed on the furnace as it should be (once a year is recommended).
Different brands of furnaces will respond differently when components fail or are in need of servicing. For example, almost all furnaces will stop heating and begin blowing cold air if the furnace filter(s) becomes too dirty or plugged. Why is this? Because a dirty or plugged filter will result in too little airflow across the furnaces heat exchanger, which will cause a temperature limit switch to fault (in order to prevent the furnace from overheating). When the furnace detects this fault, it will turn off the gas and keep the blower running in order to cool the furnace down.
