We present what we believe to be the first truly simultaneous UBVRI photopolarimetric results for a sample of eight 'normal' quasars. In five of these quasars we have not detected any measurable polarization, this result being consistent in some cases, but not necessarily in others, with the previous white light measurements of these quasars. 3C 273 is a well known low polarization quasar but, in two other cases (PG 1008 + 133 and PG 1351 + 64), we detected small (1.5 percent) polarization. In PG 1351 + 64 this polarization shows a degree of wavelength dependence, while the position angle of the polarization of PG 1008 + 133 shows a strong wavelength dependence. Some evidence of variations in the degree of polarization are found in some of the quasars in our sample.