An electronic device may generate content that is to be displayed on a display. The display may have an array of liquid crystal display pixels for displaying image frames of the content. The display may be operated in at least a normal viewing mode, a privacy mode, an outdoor viewing mode, and a power saving mode. The different view modes may exhibit different viewing angles. In one configuration, the display may include a backlight unit that generates a collimated light source and that includes a switchable diffuser film for selectively scattering the collimated light source depending on the current viewing mode of the display. In another configuration, the display may include a backlight unit that generates a scattered light source that includes a switchable microarray structure such as a switchable mirror structure or a tunable microlens array for selectively collimating the scattered light source depending on the current viewing mode.