Usually if I won't eat it I won't kill it. However a couple of years ago some squirrels got into my well house and filled it with pine cones to a depth of about two feet. I'm not kidding, there were thousands of pine cones in there and the little suckers brought 'em in one at a time!
I took my .22 out and thinned their (the squirrels) numbers a bit.
I shoot coyotes once in a while because I can get ten bucks from a local fur buyer. Of course I hunt deer, elk, bear, moose, grouse, turkey and other edibles, but other than the above the animals are safe from me.