Our house has an older furnace from 1973 that is cleaned and serviced regularly and it good shape overall, despite all the work we do on it, its still only 75% efficient. Not bad I don't think compared to our single pane double hung windows from 1945... with storms over them...
Our latest bill has winter natural gas prices on it at $1.28/gigajule. We have a combined electric + natural gas bill. Our total bill was $158 which is outstanding! We had a refund from some pipe line of $16 which helped too. The gas portion of the bill came to $57.
Our water heater and furnace are the only natural gas appliances in our home. We have electric stove, range, & dryer. We have a woodburning insert like a wood stove that we use as supplemental heat this year.
Last year, for Dec and Jan, our total bills for each month with electric and gas combined were over $400 EACH month. Feb was a little better but still $350. At least half of each bill was gas.
Like the PPs said, change your furnace filter monthly. If your furnace is older, you probably don't want to stress it out with a pleated filter. Go with the cheapies since they will allow the best airflow which doesn't put added strain on the older furnaces. If you can, get a service call so it can be checked for carbon monoxide which isn't something you want to toy around with. They will measure the air quality around your furnace and make sure its at an appropriate level. They will also clean the furnace and tune it up all for about $100 or less. $100 is a very good deal when you look at the cost of a new unit which often start around $1800. The more you can baby your antique, the better.