Dear Mr. and Mrs. Smith
Sorry to hear you are having problems with your dogwoods. Thanks for sending the photos, very helpful! It looks like some of the major limbs have died. Three major possibilities come to mind to explain this type of dieback:
1. Dogwood borer. If so, you might see sloughing bark and small holes in the trunk and branches (for more information, see http://www.clemson.edu/
2. Root problem or trunk problem, such as root rot, excessive mulch, damage to the trunk from a mower or trimmer, or physical damage to roots from trenching or grading.
3. Old age - I suspect a typical lifespan for a dogwood is two or three decades.
In any case, dead limbs should be pruned out, and then you have to decide if that leaves enough of a tree to be an attractive component of your landscape. If not, remove and replace. If you see evidence of borers, and you feel the tree is worth keeping, then you may have some treatment options.
Let me know if you have further questions.