It is very important! A dirty filter will slow down airflow and make the system work harder to keep you warm or cool - wasting energy. A clean filter will also prevent dust and dirt from building up in the system - leading to expensive maintenance and/or early HVAC system failure.
ENERGY STAR™ recommends that you check your filter every month, especially during heavy use months (winter and summer). If the filter looks dirty after a month, change it. At a minimum, change the filter every 3 months.