Polarimetry provides an avenue for probing the geometry and physical mechanisms producing optical radiation in many astrophysical objects, including stellar binary systems. We present the results of multiwavelength (BVR) polarimetric studies of a sample of historical black hole X-ray binaries, observed during their outbursts or in the quiescent (or near-quiescent) state. We surveyed both long- and short-period systems, located at different Galactic latitudes. We performed careful analysis of the interstellar polarization in the direction on the sources to reliably estimate the intrinsic source polarization. Intrinsic polarization was found to be small (<0.2 per cent) in sources observed in bright soft states (MAXI J0637-430 and 4U 1957+115). It was found to be significant in the rising hard state of MAXI J1820+070 at the level of similar to 0.5 per cent and negligible in the decaying hard state and during its failed outbursts, while Swift J1357.2-0933 showed its absence in the rising hard state. Three (XTE J1118+480 , V4641 Sgr , V404 Cyg) sources observed during quiescence show no evidence of significant intrinsic polarization, while MAXI J1820+070 is the only black hole X-ray binary which showed substantial (>5 per cent) intrinsic quiescent-state polarization with a blue spectrum. The absence of intrinsic polarization at the optical wavelengths puts constraints on the potential contribution of non-stellar (jet, hot flow, accretion disc) components to the total spectra of black hole X-ray binaries.