Caution, this is a rant. However, it's an educational one. Hopefully, someone can learn something when it comes to making sure their heating system actually heats when you turn the thermostat on. These are in no order, and are by no means the only reasons furnaces give up the ghost. All are 100% preventable with a little common sense and a few dollars spent now instead of a bucket load later.
1. Failure to maintain equipment: This should be an all-encompassing cause, but I'm writing this article; so it isn't. Not getting a tune-up, clean and check, etc will mean that your furnace will suffer cataclysmic, catastrophic failure of the worst kind. Then you can complain bitterly about the cost of a service call, parts, etc to the hapless tech who came to pick up the pieces. For the details, read on. A qualified service tech should do the work. Not all handy people are up to the task, but most of it is pretty straightforward.
2. Failure to change filters: It bears mention that any equipment that moves air will need a filter changed regularly. If I had a dollar for every time someone bought a "high performance" filter that was advertised "up to three months" my lot rent would be paid for the month. I don't care what the manufacturer says; if you have a one inch filter, change it monthly. If you have central air conditioning, change it monthly during the cooling season too. Already heard the excuse "I only use my air on really hot days." Change the filter already. You're tearing up your equipment if you don't.
3. Failure to maintain condensate drains and pumps. These need to be cleaned out twice a year to stop the traps from overflowing and ruining the sheet metal and electrical parts in your furnace. Water can also get into safety switches can create a real mess. Cleanout tees for the condensate drains to the air-conditioner are a must, but few contractors install them voluntarily. Get them to install one or find another contractor to install the equipment. Water and bleach needs to be run through the drains twice a year (easy on the bleach). Condensate pumps NEED to be taken apart and cleaned as they accumulate yeast on the inside. These will KILL the pump and will ruin a lot more than a furnace if they call it quits. 90% efficient furnace will have condensate drains that MUST be cleaned out annually.
4. Failure to have a qualified contractor and installer do the work. 90% of the reason a furnace will prompt a service call is because the installer either installed too big a furnace (failed to do a load calculation) wired the humidifier or thermostat wrong, or my favorite, didn't plumb the condensate drain lines properly. Another close relative of these are the pressure switch lines on Amana and Goodman furnaces, where they hang low enough to stop your equipment cold. Water pools in these low spots and they'll run for a week or two before setting an error code. The cure would be to shorten and reroute the line. The point is to get a trained, qualified installer to do the work. This is your home, and no place to cut corners.