There are many ways that you might notice a problem with your heating system. One of the most common is noises: clonking or clattering, buzzing or clicking, grinding or groaning. Other possibilities include poor heat circulation, rising utility bills, or short and rapid heating cycles.
Another thing that can tip you off to a furnace issue is odor. Your heating system should not smell like anything most of the time. If you do notice a smell coming from your furnace, are repairs required? Not necessarily, but some odors indicate serious problems or emergencies.