Ten years ago, I switched from a standard furnace ($1800) to a high efficiency one ($2500) and it was well worth it.

My house was so hard to heat, that I employed a kerosene heater at a lower level to help heat it. Gas bill was running around $200 a month in the winter plus about $80 for kerosene.

After switching furnaces, I no longer need to run the kerosene heater and my gas bill was cut in half. Since then gas has climbed, but the new furnace was well worth it.