This paper reports a class of stretchable electrode array capable of intimate, conformal integration onto the curvilinear surfaces of skin on the human body. The designs employ conventional metallic conductors but in optimized mechanical layouts, on soft, thin elastomeric substrates. These devices exhibit an ability to record spontaneous EEG activity even without conductive electrolyte gels, with recorded alpha rhythm responses that are 40% stronger than those collected using conventional tin electrodes and gels under otherwise similar conditions. The same type of device can also measure high quality ECG and EMG signals. The results suggest broad utility for skin-mounted measurements of electrical activity in the body, with advantages in signal levels, wearability and modes of integration compared to alternatives.