George sent in his tip of using a pulley or bearing puller to get faucet handles off of the stem without having to bang them all up. He takes out the retaining screw and puts in a headless screw to give him something for the puller to push against. Then the puller just grabs the handle and you can crank it off.
Sorry George, but the plumbing industry already caught your idea and they make very inexpensive handle pullers -- exactly the same idea but designed specifically for faucet handles, complete with a smooth shaft to go down into the screw hole to do the job. Available at most hardware stores and all plumbing stores. But then again, if you are a mechanic and you already have pulley pullers, they will be far more sturdy.