Furnaces are amazing bits of technology. They keep you warm and comfortable at a reasonable costs for decades as long as they are maintained consistently and well. Like most things if you take care of them, they will take care of you.
At the minimum remember to inspect the filters in your furnace on a monthly basis. Some types of filters should be changed once a month and some types are for a couple of months. The longer lasting filters should be cleaned every month or at least spot check to see if they are getting dirty. It is also a good idea to have carbon monoxide detectors. These should be on each floor of your home. If you already have them go ahead and check them during your monthly filter check. It is important to have these in good working order as carbon monoxide in large amounts in a confined space can be fatal. In North Carolina, landlords are required to provide these and it is a part of many local building codes.
But before doing anything to your furnace go ahead and turn off the power as well as the fuel supply. You will need to relight the pilot when you are finished. Test and inspect the belts which should not be cracked or frayed. Belt systems also should be oiled every year. Just a little oil is enough. If your system has dampers then they will probably need to be adjusted at different points in the year in order to be comfortable.
Check the flames, It is okay to leave the fuel supply on for this one. To check them remove the combustion chamber door. The flames so be steady and blue colored. If not there is something wrong with the burners and it is time to call a service company rather than trying to adjust it yourself. A full furnace inspection and cleaning is something else that should probably be professionally done at least once a year.
A good furnace will last about 18-22 years on average. If your furnace is having problems with a faulty heat exchanger, which is expensive to fix, or if your system is eating your lunch in energy costs it my be time to look at upgrading.