My great-great grandfather, Benjamin Franklin Currington, served the entire war in the 1st West Virginia Light Artillery. West Virginia issued medals for its veterans in 1866, but he had moved to Kentucky immediately after the war, and his medal was held by the WV State Department of Archives (or something like that) until a few years ago when I filed a successful claim for it, and now it's one of my most treasured heirlooms.
A great-great-great-great grandfather (note the generation gaps...), Oliver McMahan, was Captain of Company F, 30th Indiana Infantry. He died of dysentery shortly after commanding his company in battle at Shiloh. A photo of him in uniform and a letter he wrote to his wife survive.
There are others, but these are the most noteworthy.