I just moved into a home. It has central air and heating. Right now I am using heat and I noticed the outside fan is running and my neighbor's is not. Should the outside fan be blowing when using heat?

If you have a heat pump and you are using it as the heat, Yes it will run periodically, that is a normal thing. If you do not have a heat pump and it is turning then you have a problem with the electrical system that controls the AC unit.

There is a section in the sticky at the top of the forum on determining if you have a heat pump. Yes, if it is a heat pump, the outside unit runs for heat and cooling. Your neighbor may have a different system or their unit may not been running when you looked.