Spray furniture polish directly on the adhesive and rub it gently with a clean cloth. It may take several applications of the polish to remove the gunk -- if you notice it lifting, keep working at it.
Apply a small amount of nail polish remover to a cotton swab. Rub it over the adhesive to soften it, then gently scrape it away with your nail. This method is effective on permanent glue. Wipe away any remaining nail polish remover with a damp cloth.
Apply a small amount of mineral oil to the affected area, then scrub it with a clean cloth. Wipe away any leftover oil once the adhesive has lifted.
Apply a commercial adhesive-removal product that's deemed safe for use on wood products. Apply the product as directed and wipe away any leftover residue with a clean cloth.