Electronic devices may include displays. A display may include display layers having an array of display pixels and a backlight unit that provides backlight illumination to the display pixels. The backlight unit may include a light guide plate that distributes light across the display layers and a stack of optical films that may be used to enhance backlight performance. The optical films may be interposed between the light guide plate and the display layers. The light guide plate may be provided with one or more rounded edges formed from curved surfaces and/or one or more beveled edges formed from chamfered surfaces. Providing the light guide plate with rounded or beveled edges may minimize abrasive contact between the light guide plate and the adjacent optical films. An injection molding tool may be used to mold a light guide plate with rounded or beveled edges.