We are in the process of surveying the linear polarization in luminous, early-type stars. We here report on new observations of the B [e] stars S 18 and R 50, and of the Luminous Blue Variables HR Car, R 143, and HD 160529. Together with previously published data, these observations provide clear evidence for the presence of intrinsic polarization in 1 B[e] star (HD 34664) and in 5 LBVs (ν Car, P Cyg, R 127, AG Car, and HR Car). The data indicate that anisotropic stellar winds are a common occurrence among massive stars in these particular evolutionary stages. For such stars, mass-loss rates estimated using the assumption of a spherical, homogeneous and stationary outflow may be in error.