There are two opposing views on this question. Choose the one that suits your personality and your library.
Some librarians take off the labels and stickers that are easy to remove and don’t worry about the rest. Use a handheld hair dryer to melt and loosen the glue, and then remove the stickers with Scotty peelers (or a fingernail).
Librarian Kristi Stansfield says, “Life is too short and time is valuable. Removing all that stuff can be so time-consuming. I would rather spend my time on other tasks.” You can place your own stickers and barcodes over the top of the original library sticker and call it done.
Librarian Laura Carr says, “To avoid confusion, I don’t want any other library markings on my books. I remove outside stickers as part of my cleaning process and put my own mylar and spine label on. Then I white-out any library stamps on the inside of the book and cover the white out (when dry) with a plain white Avery label.” Using this procedure will help to insure that none of your library books are returned to the library that discarded them in the first place.
Librarian Sherry Early has used Un-du or Goo-gone to remove stickers and sticker residue from hardcover books. (Be sure to test the chemicals you use on some unobtrusive corner of the book first because sometimes these chemicals will take off the ink from some book cover surfaces.) However, another book lover recently introduced Sherry to this citrus air freshener product, Pure Citrus Orange, available only at Walmart, as far as we know. Use it with a damp cloth to take off stickers and sticker goo. It also will help erase permanent marker from book covers. And it smells good.
You can use fine sandpaper to lightly sand off library stamps or foxing on the top or side of the book’s pages. You will want to clamp the page block tightly so the pages stay straight and so that you don’t bend them as you’re pressing down. One librarian used 220 Very Fine finish sandpaper to do this, and it removed the library stamp almost completely.