If you're fairly handy, you could service your own gas fireplace at the start of the season, especially if the fireplace is more of an asthetic feature rather than a heat source. Gas fireplaces require complete annual disassembly and cleaning to keep them operating efficiently.
A handy homeowner could also start his own furnace, but if you want to do it right, you'll need to know how to use a volt/ohmmeter. You'd also want to have access to a Carbon Monoxide analyzer. Before starting your furnace for the season, you'll want to do more than just blow out the fan blades and wiping down the burners.
If you don't clean and service the furnace properly, it would probably be fine for a while; problems may not show up in the beginning. Just like a car, you don't have to change the oil regularly. But if you don't perform some maintenance, it will shorten the life of the equipment overall. With newer furnaces, the safety circuits in particular need to be tested; one is a flame sense circuit. If the flame sensor fouls, the burners don't stay lit and you have no heat. This is the #1 reason I get calls at 3:00 am.
Ideally, furnaces should be professionally inspected and serviced annually. If you take your car to a shop for an oil change every three thousand miles, why wouldn't you have the main heating appliance in your home tuned up before the dangerous cold sets in? The annual inspection and service schedule is also suggested for a gas fireplace, if you rely on it for heat. If it's more of an ambiance type fireplace, we suggest that you have it professionally inspected and serviced every two or three years, depending on usage.
On occasion I have to pull and clean the blower and fan, at the cost of a few hundred dollars, for a homeowner who thought he'd done a pretty good job of cleaning and maintaining his own system. At that point, they sometimes realize that it can be cheaper and more convenient to simply have the furnace professionally serviced at the start of each heating season.