An electronic device such as a head-mounted display may have a display system that produces images. The display system may have one or more pixel arrays (26-1, 26-2) such as liquid-crystal-on-silicon pixel arrays. Images from the display system may be coupled into a waveguide (116) by an input coupler system (114X, 114Y) and may be coupled out of the waveguide in multiple image planes using an output coupler system (120X, 120Y). The input and output coupler systems may include single couplers, stacks of couplers, and tiled arrays of couplers. Multiplexing techniques such as wavelength multiplexing, polarization multiplexing, time-division multiplexing, multiplexing with image light having different ranges of angular orientations, and/or tunable lens techniques may be used to present images to a user in multiple image planes.