I just bought a new stove and it smells like something is burning in  my home.

There is break-in period with all new stoves called the curing process.  It is something like the smell inside a new car except the smell is not as pleasant.  The burning allows the paint to harden and adhere to the steel.  There is a different process for wood and gas stoves-refer to your manual.

I have had my stove for years and it smells like something is burning in my home.

This may be the burning off of summer debris that has built up over the warmer months.

I have a fireplace that is giving off a terrible smell and I am not even burning?  What can that be?

It is called "Cold Air Inversion".  This generally occurs during the winter months and is caused by cold air sinking down the chimney over the creosote pushing the smell into the house.