Electronic devices are provided that communicate over cables and other communications paths that include optical and electrical paths. A cable may include wires for forming an electrical path and one or more optical fibers for forming an optical path. Connectors at one or both ends of the cable may include electrical contacts and an optical coupling structure associated with the optical path. Optical paths may be included in connectors such as tip-ring-sleeve connectors and connectors of other types. Interface circuitry may be included in a connector to convert between optical and electrical signaling schemes. Wavelength-division-multiplexing may be used to support bidirectional communications. Breakout boxes and other equipment may be connected using the cables. Digital signals such as digital noise cancellation signals may be conveyed over the optical paths. Power and other electrical signals may be conveyed over the electrical paths.