Spectropolarimetric observations are presented for 21 AGB stars, 13 proto-planetary nebulae (PPNs), and two R CrB-type stars. The spectra cover the wavelength range from ~4200 to 8400 A with 16 A resolution. Among the AGB stars, 8 of 14 M giants, five of six carbon stars, and zero of one S star showed intrinsic polarization. At least 9 of 13 PPNs exhibited intrinsic polarization, while the R CrB-type stars show intrinsic polarization during fading episodes. There is a statistical correlation between mean polarization, P, and IR color, K - [12], among the AGB stars such that redder stars tend to be more polarized. The PPN sample is significantly redder and more polarized, on average, than the AGB stars. This increase in P with increased reddening is consistent with an evolutionary sequence in which AGB stars undergo increasing mass loss, with growing asymmetries in the dust distribution as they evolve up and then off the AGB into the short-lived PPN phase. A related trend is found between polarization and mass-loss rate in gas, gas. The detectability of polarization increases with mass-loss rate, and probably all AGB stars losing mass at >10-6 M☉ yr-1 have detectable polarization. Multiple observations of three polarized AGB stars show that in some cases P increases with mV, and in others it decreases. If polarization arises from scattering of starlight off an aysmmetric distribution of grains, then the distribution varies with time. Polarized features are detected in the TiO bands of three M-type Mira variables, in the CN bands of the carbon stars R Lep and V384 Per, and in the Swan bands of C2 in R CrB and two PPNs. Polarization effects in the molecular bands appear to be more common and the effects are larger in O-rich than C-rich objects.