When heating your home, what position should the fan switch be on, auto or on?

On will make the fan / furnace run all the time, auto will turn it on when the temperature drops below the set temperature. Auto is usually what you want.

Its all up to you what you want to leave it on, sometimes people find it better to leave it in the on position cause it circulates air throughout the house continuosly, but then again its totally up to you, it doesn't have to be set on a certain one for your heat to come on

It will make the fan blow all the time but it will not turn the furnace on until the tstat calls for it

Leaving it in the on position will just wear out the fan motor quicker and also waste more electric. Put it in the auto position for maximum electric savings.

Personal choice

Many times a fan left in the on position will help to distribute the air more evenly in the home. If you have a electronic air cleaner a the fan running all the time will be of benefit.
Modern electric motors have a long life expectation and in many cases it is easier on the motor to let it run all the time instead of constantly starting and stoping. Motor starting is especially difficult on the windings until the motor gets to design speed.

All three blower motors in my house run 24X7. I use Fanhandlers to adjust the speed to the load. The motors are all at least 15 years old and the only service they get is a annual oiling. These are sleeve bushing motors and not the more expensive ball bearing units.

If your air duct both supply and return are sized correctly there will be very little load on the blower motors allowing them to last almost forever.

I agree with hvac1000 and youcantstop48. I have a four year old system and run my blower all the time year round the same blower motor is rocking on. If your more comfortable with it running let it run if the noise is bothersome cycle it with the heat and air, it is made to run all the time if you want. I choose to run my blower all the time to filter the air.