Can I refuse to sign for a delivery if the goods look damaged?

You are generally entitled to inspect goods, or at least their outer condition, before accepting delivery, and noting damage at the time of delivery is important evidence for any later claim. You can refuse to sign an unqualified acceptance, and instead sign with a clear written note, such as recording that the packaging appeared damaged, or in serious cases refuse the delivery altogether and ask the courier to return the item to the sender, depending on the courier's own procedures. Signing a delivery docket as received in good order without qualification can make it more difficult to later claim that the goods were damaged in transit, since carriers often rely on such signed confirmations as evidence. Take photographs immediately, before and after opening if possible, and notify the sender and the courier in writing as soon as you discover any damage, since transport claims often have short notification windows.