A cryogenic technique has been used to produce polarized He-3 targets of up to relative density p = 12 atm (almost-equal-to 3 x 10(20) He-3 atoms/cm3; p = 1 atm corresponds to 760 Torr or 101.3 kPa pressure at 273 K). In these targets He-3 nuclei are polarized by spin-exchange collisions with optically pumped rubidium atoms. From transmission measurements at wavelengths of 790-800 nm, we have determined pressure shifts, linewidths, and line-shape asymmetries for the Rb 5S1/2 --> 5P1/2 D1 transition. The Rb spindestruction rate was found to exhibit a quadratic increase versus He-3 pressure, which indicates the importance of Rb-He-3-He-3 collision processes. The transmission results for circularly polarized light are well described by a model that predicts the dependence of the average Rb polarization on Rb density, He-3 pressure, light intensity, and cell geometry. The Rb-He-3 spin-exchange cross section, <sigma-SE-upsilon> = 6.1 x 10(-20) cm3 s-1, was found to be independent of He-3 pressure up to p = 12.1 atm. Maximum He-3 polarizations of 72-79% were observed with cells of 17 cm3 volume that contained He-3 at p = 6-9 atm.