Yes
Under normal ambient conditions, only certain metals exhibit "ferromagnetism"... the intrinsic ability to respond to a magnetic field without being subject to an applied current. Iron, nickel, and cobalt (and some alloys composed primarily of these) will all act as "permanent magnets" and can all be picked up by either permanent magnets or electromagnets. Also, certain "rare earth" elements (especially niobium) are ferromagnetic. All other elements, metallic or otherwise, are not susceptible to ferromagnetism. However, when cooled to very low temperatures, i.e. near absolute zero) some materials that do not normally exhibit magnetism will begin to do so. There are also other forms of "magnetic behavior" (paramagnetism, diamagetism), etc. can be observed in many other materials that are not, themselves, ferromagnetic. Ferromagnetism, however, is by far the strongest of the family of magnetic forces, and is that with which most of us have daily experience.