I have a weathermaker 8000 furnace and the fan motor runs constantly even when the heating cycle is done. I do not have a/c installed and I cannot locate a fan only switch.

Is this normal for this unit?

Not normal.

Is the thermostat blower switch (if equipped) set to on or auto?

There is a blower fan control on all furnaces. Its job is to hold off the blower until enough heat is in the heat exchanger then it turns the blower on. Same thing when the heat is gone it turns the blower off.

Different units can use different types of controls.

Look on the inside of the blower door for a wiring diagram and location.
Some have a button that you push to turn the blower on all the time and some do not. Check for this type of control first.

If your furnace is a newer model it is controlled by a circuit board and sensors/heat sense disks.

A complete model number from you would be great since they made 100 different units that are called 8000 series. My crystal ball is broken so I cannot tell your EXACT model number from here.