A wireless power transmitting device may have an array of transmitting coils to transmit power wirelessly to a wireless power receiving device having an array of wireless power receiving coils. The receiving device may have a rectifier that receives alternating-current signals from the wireless power receiving coils and provides corresponding rectified direct-current voltage signals to a capacitor and other circuitry. The rectifier circuitry may include bridge circuits each of which is coupled between a respective coil in the array of wireless power receiving coils and the capacitor. The wireless power transmitting coils may be arranged in a hexagonally tiled array. The wireless power receiving coils may include first, second, and third coils that are aligned with respective vertices in an equilateral triangle having sides with lengths equal to half of the center-to-center spacing of the hexagonally tiled transmitting coils.