An organic light-emitting diode display may have an array of pixels. Each pixel may have an organic light-emitting diode with an anode and cathode. The anodes may be formed from a patterned layer of metal. Thin-film transistor circuitry in the pixels may include transistors such as drive transistors and switching transistors. Data lines may supply data signals to the pixels and horizontal control lines may supply control signals to the gates of the transistors. A switching transistor may be coupled between a voltage initialization line and each anode. The voltage initialization lines and capacitor structures in the thin-film transistor circuitry may be formed using a layer of metal that is different than the layer of metal that forms the anodes.