It is OK to leave the piolt on. There is some benefit to this if the furnace is located in a damp basement. It will keep the pilot assembly dry. The only drawback is the add fuel cost.

There may not be any financial penalty for the off months if there is a minimum monthly charge for gas service.

mike home pretty much hit the nail on the head. And to add to that, the little bit xtra it might cost you in gas (at this time anyhow) will far pay for itself in the long for just the reasons he stated.
I'm certain there will be a few who may disagree but, after over 30 some years in the business, I can tell you the frequency of maintenance and associated costs with the newer gas ignition systems far outweigh the cost of leaving the pilot light on. The pilot light keeps everything dry and ready to fire up when needed. Sure, there are instances when a thermocouple might go but they are way cheaper than an electronic ignition. Yea, the pilot light just might blow out in a rare instance but for the most part, you'll be fine leaving it on. The idea of doing away with the pilot light was to fall in line conserving energy so more gas will be available to more people. Many may disagree, and I expect that but, the only person who loses with the energy conserving is the consumer. Since it makes more gas available to more people, the utility can add more customers and the the national usage goes up overall. And due to the maintenance and failure rates of the current gas ignition systems and circuit boards, it does keep more companies busy making money so maybe overall the economy, at your expense if you have one, moves a little bit.

Thanks for the feedback. That's what I was hoping to hear. We moved into our house last year. It's an older furnace and probably hasn't been serviced in several years, but seems to work fine. I spoke to a friend who used to service furnaces and I asked him if it was necessary to have some one look at this one and he said that basically if I change the filter regularly and it's not making any funny noises, I should be ok.

Interesting discussion. I had two houses with gas furnaces with standing pilot and AC. I assumed that in the Summer the AC would cause the flue gas from the pilot to condense in the heat exchanger and also would add slightly to the load on the cooling. So one of them has been replaced with a hot surface ignitor. Loved the reduction in gas bills. Last fall the unit would not light, 7 years old. Bad (Johnson Controls) control board. The technician could not test the board directly but checked everything else. Used Honeywell universal board. Charge for repair $345.00. Now I probably could do the other tests myself. Assuming that the pilot uses $5.00 of gas per month, the hot surface ignitor seems to be a reasonable choice- but not foolproof not trouble free.