Removing stickers from harder, less porous surfaces, such as wood, plastic or metal is usually easier than removing stickers from cardboard; however, with extra patience and the right household product you can remove stickers from cardboard---and you can do so without tearing a chunk of paper out of it and without leaving a big, oily stain. You will need few tools and a minimal amount of time.
Saturate a cotton swab or cotton ball with rubbing alcohol; if you have a large area of tape to remove it's easiest to use a cotton ball. Rub this over the tape, wetting it. Alcohol evaporates quickly and should not harm the cardboard. However, if the cardboard is printed, some of the ink may fade.
Let the alcohol sit on the tape for 1 to 2 minutes. Use a razor knife to lift one corner of the tape.
Apply more alcohol to the tape---especially the edges---if it's not removing easily. The more alcohol you can get on the adhesive side as you pull the tape up, the better; the alcohol is a mild solvent and will help dissolve the adhesive.
Apply more alcohol to any remaining sticker residue. Wipe the box with a clean, dry cloth or paper towels when all of the sticky residue is gone.
If the sticker is too large to quickly cover using a cotton ball, pour the alcohol on a clean rag and wipe this over the sticker. If you have cuts or scrapes on your hand, you might want to wear rubber gloves when using rubbing alcohol. Alcohol won't hurt you, but it will sting.
Do not yank the tape up---pull gently to avoid pulling pieces of the cardboard with it. Oil-based adhesive removers work well for some surfaces but can leave oily stains on cardboard. For best results, use rubbing alcohol.