Although algae are not necessarily harmful to swimmers, it does create an eyesore as well as an unpleasant swimming environment.  Also, if neglected over a long period, bacteria associated with algae can be a health concern. Algae growth not only looks unsightly but is considered a hazard to public health because it can attract mosquitoes and other insects. Because algae growth becomes a host for various pathogens, any signs of growth should be treated without delay.
In regards to harming your equipment,  running the filter when the pool is covered with algae can clog up the filter and even damage it permanently. Pool owners must be careful to remove algae to prevent damage to their equipment.