We present results of optical polarization observations performed with the MASTER robotic net (Lipunov et al., 2004AN....325..580L, 2010, Advances in Astronomy, article id. 349171, 1; Kornilov et al., 2012, Exp. Astron., 33, p. 173) for three types of objects: gamma-ray bursts, supernovae, and blazars. For the Swift gamma-ray bursts GRB100906A, GRB110422A, GRB121011A, polarization observations were obtained during very early stages of optical emission. For GRB100906A it was the first prompt optical polarization observation in the world. Photometry in polarizers is presented for Type Ia Supernova 2012bh during 20 days, starting on March 27, 2012. We find that the linear polarization of SN 2012bh at the early stage of the envelope expansion was less than 3%. Polarization measurements for the blazars OC 457, 3C 454.3, QSO B1215+303, 87GB 165943.2+395846 at single nights are presented. We infer the degree of the linear polarization and polarization angle. The blazars OC 457 and 3C 454.3 were observed during their periods of activity. The results show that MASTER is able to measure substantially polarized light; at the same time it is not suitable for determining weak polarization (less than 5%) of dim objects (fainter than 16m). Polarimetric observations of the optical emission from gamma-ray bursts and supernovae are necessary to investigate the nature of these transient objects.