How do I get price tags off of books?

If it's a paper sticker tag you can use  rubber cement thinner. Using a cotton swab wet the sticker to the point of absorption. Let it soak in for a few seconds and the very carefully peel off the sticker. If the sticker appears to be tearing the cover wet the  sticker again and start from the opposite side. You want to start at the opposite side otherwise you may tear the loose piece of cover off. If the sticker is plastic you'll probably need to use a warm iron or hair blow-dryer, unless you can get the thinner underneath the sticker. I've used the thinner on many cover and have had a light stain on only a few. In cases where I had a stain it was due to the stickers glue and not the  thinner.

You can also use a warm iron on the sticker and remove the sticky residue with the thinner. This method also works on Scotch, masking and white tape. I prefer to use the rubber cement thinner first if it  works because heating the masking and white tape leaves a messy residue to remove. When working with tapes try not to put the iron directly on top of the tape. Usually holding it a ½ inch above will suffice. For large areas of cleaning use may wish to use a cotton ball.