We replaced the gas furnace on the current house last March. From early March until the end of the heating season we saved almost $300+ compared to the previous year. With the federal and provincial energy savings grants, we got a rebate of almost $1500 on the installation.
The replaced furnace was original to the house (1985), had a single stage and a single speed fan motor. It tested out at 46% efficient, and had pin holes in the heat exchanger, so combustion gas was starting to leak through.
The new furnace is a high efficiency (97%) Trane, with a two stage burner and a variable speed DC fan motor. Huge difference in how comfortable the house is. Leaving the fan on all the time had very little impact on the electricity bill, but we no longer feel the swings in temperature that we used to. And our revised annualized gas bill is now $84/month.
I usually get the furnace cleaned once every year or two.