I did get my state forester out to my place, and also read much on the subject, and the recommendation for most hardwoods was 8 to 10 feet spacing, and 6 feet for some (poplars I think are in that group) for the reasons that others mentioned-- they will grow up faster instead of wasting energy spreading, and they will be straighter as well. Then cull them as needed. The white pines you mentioned probably should have been culled about 20 years ago.
If the trees aren't planted for harvesting, I don't think spacing matters as long as you plan for competition, i.e., don't plant the persimmons were they will soon be shaded by the taller, faster growing trees.