Running HVAC without filters?

[Paul Sian]

I recently bought a 4 unit multifamily.  When going through with the home inspector I saw the furnaces did not have any filters in them.  It was warmer at the time and since they were not being run I did not think too much about it.  Went to the building shortly after closing and saw they were running without filters.  I have always learned that the furnaces need to be run with filters and I did go out and buy some for the furnaces.  All the furnaces are new due to the old ones being damaged beyond repair due to a flood.  While I plan to use filters I was just curious does anyone run their furnaces without filters?  What kind of harm could happen as a result?

Thanks