Furnace Fan Won't Stop Running!

The fan is probably connected to a "fan limit switch". This would be a junction box with a tubular shaft sticking into the plenum and would have one or two cables attached to it. It turns the fan on when the air in the plenum is hot enough, then turns it off once the air cools down, and also shuts off the burner if the air gets to hot. Here is a link to a picture of one:

I agree with that, but it seems to me the furnace fan should be controlled by the service switch. Maybe they did it differently

Also, it might be useful for the OP to know that the fan limit switch generally controls a relay rather than control the fan directly, and that limit switches are adjustable -- if the shutoff temp is too low, the fan might never shut off.

My guess is that Peggy is not going to dig into any wiring on the unit. If she can find the control, she may find an adjustment on it that was touched by someone, causing it to run continuously, and correct it

I fully agree. The furnace switch is supposed to shut off EVERYTHING on the furnace. I'd start by getting that switch checked and/or rewired.

On your thermostat, there could be a small switch (usually on the bottom), that says FAN. Did someone bump it to the ON position? That switch is there so you can run the fan all the time, or turn it on in the summer to circulate the air in the house.

As others said, the Fan-Limit switch would be your cause if none of the above apply. They're pretty each to replace and not costly. Of course you got to get one that will fit. Those devices also may have a switch on them to turn the fan on manually. If someone changed a furnce filter or something, did they bump that switch?

Sounds like a sticky relay. What's your experience with things electrical? Done a bunch of troubleshooting? got a wholesale supply line for furnace parts?