An electronic device may have a housing formed from a rigid material such as metal or fiber-composite material. A display such as an organic light-emitting diode display may be attached to a planar wall portion of the housing using a layer of adhesive. A display cover layer may be attached to the organic light-emitting diode with a layer of adhesive. The adhesive layers may be rigid to enhance device stiffness. The housing may have curved sidewall portions that extend outwardly from the planar wall portion to enhance stiffness. The organic light-emitting diode display may have an array of pixels formed from thin-film transistor circuitry. The thin-film transistor circuitry may be formed on a substrate such as a glass substrate that is attached to the planar wall portion. The organic light-emitting diode display may have a circular polarizer that is attached to the thin-film transistor circuitry.