If Lyme Disease is epidemic in your area or if ticks are plentiful, use mulch very sparingly and keep the yard free of leaves because excess ground moisture and shelter might invite nomadic ticks to take up residence.
Studies show that the type of mulch used can either attract, repel or cause lethality to insect pests. House ants are attracted to pine and cypress mulch, although they are repelled by the aroma of cedar, while Formosan subterranean termites are killed by mulches made from the tea tree. Wood chips and shredded bark, particularly when new and un-weathered will cause termites to either leave the area or starve, so apply aromatic barks to combat both ants and termites.
As termites are and probably always will be, a part of the natural landscape, mulches should be kept away from structural foundations which could serve as a freeway of moisture into the soil, inviting pests right into your home.
In short, there is no one mulching solution for every locale and every pest so consult your county agricultural extension agent for best practices and ask your neighbors what works for them.