A drop of oil on the arm bearings every month is all I do. Zachary Taylor says:
"Scroll saws are simple machines that require little in the way of servicing... Clean and lubricate the moving parts regularly. Bearings in pivot points require more lubrication than others... all parts that rub against others are subject to potential wear... careful inspection should reveal these parts."
He then has photographs of various scroll saws being maintained, including a Diamond which is having its motor spindle lubricated and a saw which is having dust around its motor housing and fan blown away by a bicycle pump. Some saws (eg Diamonds) are belt driven and he says these should be checked regularly for tension, seating and signs of wear.