An electronic device may have optical sensors. Control circuitry may use sensor measurements in controlling adjustable components and taking other actions. The optical sensors may be self-mixing sensors such as incoherent self-mixing sensors. One or more sensors may be used in gathering sensor measurements. In configurations in which an electronic device contain multiple self-mixing sensors, multi-wavelength measurements can be gathered using incoherent light sources in the sensors that operate a set of different wavelengths. The light source of each incoherent self-mixing sensor may be a superluminescent light-emitting diode, a resonant cavity light-emitting diode, or other amplified or non-amplified spontaneous emission source. Optical systems such as lenses in a housing for an electronic device may be aligned with the self-mixing sensors. Self-mixing sensors may serve as proximity sensors, sensors for detecting touch input, sensors for measuring spectrums associated with targets of unknown materials, displacement sensors, or other sensors.