The United States and Mexico have a joint migratory bird treaty that requires our states to set a closed season on crows. Apparently this is because there are some species of crows in Mexico that are considered threatened. However, the state laws generally provide that crows may be shot out of "season" if they are seen to be depredating, or about to depredate, farm crops, fruit or nut trees, etc.
Personally, I have never seen a crow that was not depredating, about to depredate, or thinking about depredating something.
I watched a crow take a mouse, once and I wouldn't call harassing hawks depredation, but otherwise they are very destructive.