Termites are by far the most damaging of the wood destroying insects.  They have a long lifespan and the colonies can number in the thousands.  All homes should be inspected for terminates and other wood destroying insects.

Carpenter Ants

In New Jersey the black carpenter ant is the only species important to homeowners.  Attracted to water softened wood there damage can be extensive as they search for nesting sites.  

Other wood destroying insects

Carpenter bees, powder post beetles, Old house borer beetles  

Although difficult to detect at times these other wood destroying insects can become a problem