Should be cleaned once a year. In all cities and many towns, there are firms which have special motorized vacuum equipment which does the work efficiently.
Clean burners in gas-fired boiler and flush fuel oil storage tanks to remove sediment. Remove rust.*
(Source: Watkins Household Hints, 1941)
*Note - We have different furnaces now so much of this tip is not valid. It is however still advisable to have a professional tune up and clean your furnace, chimneys, etc. I do it once a year - furnace in the fall and air conditioner in the spring. Chimney every 1 to 2 years depending on how often I use the fireplace.