The remanent states and hysteretic behavior of thin-film magnetic rings has been investigated experimentally and by micromagnetic modeling. Rings of diameters 160-520 nm, made from Co using lift-off processing, show three distinct remanent states: a vortex state, an "onion" state with two head-on walls, and a "twisted" state containing a 360degrees wall. The range of stability of these states varies with ring geometry, with smaller width rings showing higher switching fields and greater variability.