We report the first extensive study of stellar Rb abundances. High-resolution spectra have been used to determine, or set upper limits on, the abundances of this heavy element and the associated elements Y, Zr, and Pa in 44 dwarfs and giants with metallicities spanning the range -2.0 < [Fe/H] < 0.0. In metal-deficient stars Rb is systematically overabundant relative to Fe; we find an average [Rb/Fe] of +0.21 for the 32 stars with [Fe/H] < -0.5 and measured Rb. This behavior contrasts with that: of Y, Zr,and Ba, which, with the exception of three new CH stars (HD 23439A and B and ED + 5 degrees 3640), are consistently slightly deficient relative to Fe in the same stars; excluding the three CH stars, we find that the stars with [Fe/H] < -0.5 have average [Y/Fe], [Zr/Fe], and [Ba/Fe] of -0.19 (24 stars), -0.12 (28 stars), and -0.06 (29 stars), respectively. The different behavior of Rb on the one hand and Y, Zr, and Ba on the other can be attributed in part to the fact that in the Sun and in these stars Rb has a large r-process component while Y, Zr, and Ba are mostly s-process elements with only small. r-process components. In addition, the Rb s-process abundance is dependent on the neutron density at the s-processing site. Published observations of Rb in s-process enriched red giants indicate a higher neutron density in the metal-poor giants. These observations imply a higher s-process abundance for Rb in metal-poor stars. The calculated combination off he Rb r-process abundance, as estimated for the stellar Eu abundances, and the s-process abundance, as estimated for red giants, accounts satisfactorily for the observed run of [Rb/Fe] with [Fe/H].