Three rare-gas halide (RgX(-)) anions, KrBr-, XeBr-, and KrCl-, and the corresponding neutral, open-shell van der Waals complexes are studied with anion zero electron kinetic energy spectroscopy. The spectra for each system reveal well-resolved progressions in the low frequency vibrations of the anion and one or more of the three neutral electronic states accessed by photodetachment, providing a detailed spectroscopic probe of the Rg-X- and Rg-X interaction potentials. In the case of KrBr-, transitions to all three of the "covalent" neutral electronic states (the X1/2, I3/2, and II1/2 states) were observed. For XeBr-, transitions to the X1/2 and II1/2 neutral states were observed. For KrCl-, only the X1/2 state could be studied. From our data, we construct model potentials for the anion and each observed neutral state, and these are compared with other experimental and theoretical potentials.