Answer:
It depends mostly on how strong the magnet is and how much iron, nickel, cobalt is in the substance its supposed to stick to, as these elements are the only common substances that readily stick to magnets, except other magnets or electromagnets. A premium quality, N45 purity neodymium based permanent magnet in the form of a 1 inch x 1 inch x 1 inch cube, for example, can pull a another magnet of the same type several inches away and steel staples as far away as a hand length (the length between the tip of your thumb and the tip of your pinky, with all your fingers spred out). On the other hand, a magnetite refrigerator magnet (about the worst type of magnet there is) would have to be less than half an inch away from steel staples to attract them.
Keep in mind that the actual range of a magnetic field is infinite, but because of the physical properties of such fields, their strength is only noticeable when very close to their source. Therefore, the "significant" range of a magnetic field depends on how strong its source is.