In general a polymer can be broken down into two areas. Thermoplastic and Thermoset.
A thermoplastic material can in theory be heated and formed and re-heated and formed an infinite number of times. In practice this isn't exactly true as during normal processing and reheating process degradation is usually evident within the material. This in turn gives a decrease in mechanical properties as a plastic is reheated. Thermoplastics are generally the commodity plastics at present due to there easy processing characteristics and general low costs. Such materials include nylons, polypropylene's, PE's, ABS, polystyrene's and polycarbonate's to name a few.
Thermosets however cannot generally be reformed, this is due to a change which takes place under heat and pressure. This change produces cross links within the material which in turn keys the polymer chains together and thus removes any opportunity for the material to be reformed. Such examples can include Urea formaldehyde, phenol formaldehyde and natural rubber.