We report the observation of interspecies Feshbach resonances in an optically trapped mixture of Rb-85 and Cs-133. We measure nine resonances in the lowest spin channel for a magnetic field range from 0 to 700 G and show that they are in good agreement with coupled-channel calculations. The interspecies background scattering length is close to zero over a large range of magnetic fields, permitting the sensitive detection of Feshbach resonances through interspecies thermalization. Our results confirm the quality of the Rb-Cs potential curves [Phys. Rev. A 85, 032506 (2012)] and offer promising starting points for the production of ultracold polar molecules. DOI:10.1103/PhysRevA.87.010703