Novel cylindrical dielectric resonator antennas (DRAs) having supershaped base contour and adopting plastic materials for the resonator are studied. The specialization of the supershaped DRAs to the generation of linearly and circularly polarized waves is discussed, analyzed and experimentally verified. The resulting antennas exhibit wide-band (WB) performance in terms of input impedance matching, radiation patterns, realized gain and polarization properties. The proposed class of antennas shows broadside radiation with broad and smooth patterns stable over frequency, efficient and stable radiation and wide matching bandwidths. These antennas can potentially find application as access points for indoor multimedia radio systems.