The most expensive part of a furnace is the blower motor. Suppose the blower motor breaks down due to any reason it almost costs about $1000 to be replaced or repaired.
The price may vary according to the model of the furnace.
Secondly, the thermostat and the circuit board are two such parts of the furnace which are quite expensive to replace.
Especially the thermostat is one of the most fragile parts of the heating system and must be handled with utmost care.
Slight negligence might cause the part to blow off. Once gone out of order, it has to be replaced with a new one.