Quantum interference effects in rings provide suitable means for controlling spin at mesoscopic scales. Here we apply such control mechanisms to coherent spin-dependent transport in one- and two-dimensional rings subject to Rashba spin-orbit coupling. We first study the spin-induced modulation of unpolarized currents as a function of the Rashba coupling strength. The results suggest the possibility of all-electrical spintronic devices. Moreover, we find signatures of Berry phases in the conductance previously unnoticed. Second, we show that the polarization direction of initially polarized, transmitted spins can be tuned via an additional small magnetic control flux. In particular, this enables to precisely reverse the polarization direction at half a flux quantum. We present full numerical calculations for realistic two-dimensional ballistic microstructures and explain our findings in a simple analytical model for one-dimensional rings.