Here in Florida the red-bellied woodpecker makes up the third member of the "Big Three" on my enemies list. The raccoon and grey squirrel being the other two. Trapping and shooting controls the mammals pretty well, but the woodpeckers have the advantage of sheer numbers. Very destructive birds!
Crows, being very smart, get the message quickly when you make an example of one of them. I shoot the lookout while the others are busily engaged in raiding my lychee and loquat trees. After that, they'll avoid even flying over my property for a year or two. Flocks of common grackles used to be a problem when I was growing citrus, but since I lost all my citrus to greening disease years ago, they tend to leave my other fruit alone.