Despite recent progress in bendable and stretchable thin-film transistors using novel designs and materials, the development of conformal devices remains limited by the insufficient flexibility of devices. Here, we demonstrate the fabrication of graphene-based conformal and stretchable devices such as transistor and tactile sensor on a substrate with a convoluted surface by scaling down the device thickness. The 70 nm thick graphene-based conformal devices displayed a much lower bending stiffness than reported previously. The demonstrated devices provided excellent conformal coverage over an uneven animal hide surface without the need for an adhesive. In addition, the ultrathin graphene devices formed on the three-dimensionally curved animal hide exhibited stable electrical characteristics, even under repetitive bending and twisting. The advanced performance and flexibility demonstrated here show promise for the development and adoption of wearable electronics in a wide range of future applications.