A whole lot depends on the part of the country your are in. Down here in FL, possums and skunks don't get bothered. Coons, however are another story. They carry a serious rabies threat and we kill every one we see. Coyotes are the same.
I like seeing a few squirrels in the back yard - so do the neighbors. However, when they start getting too numerous they eat through the pool screens. Then they need to get thinned out. We'll shoot enough to get down to a couple per yard.