Believe it or not, one of the most common problems is that your thermostat is not turned all the way on to either heating or cooling.
Check and clean the furnace filter. When the filter gets too dirty, then the air becomes restricted, overheating the heat exchanger and kicks the furnace off.
Air conditioners are sized to maintain temperatures. If you let your home get too hot while you are away it could take several hours to cool to a comfortable level. It is not a good idea to turn your thermostat up too high when you are not there.
Make sure your filter is cleaned once per month. Close all your foundation vents in the winter and open them in the summer. Close your fireplace damper when not in use. Open drapes in the winter when the sun is shining. Close your drapes in the summer to eliminate extra heat gain. Shut off all appliances, computers and media equipment when not in use.
Now is the best time to upgrade your older equipment. With the bailouts from the government, there were Federal tax dollars designated for higher efficiency equipment. Up to 30% in some cases. Some power companies offering huge rebates towards the purchase of select high efficient furnaces and heat pumps. Couple those with the manufacturer discounts and it really adds up to a smart decision made to upgrade.