A furnace-installable electrostatic system puts a high-voltage charge on the air passing through it. Dust, pollen and microbes become attracted and stick to a removable filter. Depending on the amount of material it collects, you may have to clean or replace it every few weeks.
High-performance furnace filters with the same dimensions as your standard filter do a more thorough job of cleaning the air. Though they cost more than a regular filter, you don't need to modify the furnace. Because they have a finer mesh cross-section than standard filters, they reduce the airflow through the furnace.
You can find ultraviolet (UV) lamps designed to fit inside the furnace. These do not remove particles, but they kill airborne microbes with ultraviolet light. They consume about 10 watts of electricity.