A variety of nanoscale photonic, mechanical, electronic, and optoelectronic devices require scalable thin film fabrication. Typically, the device layer is defined by thin film deposition on a substrate of a different material, and optical or electrical isolation is provided by the material properties of the substrate or by removal of the substrate. For a number of materials this planar approach is not feasible, and new fabrication techniques are required to realize complex nanoscale devices. Here, we report a three-dimensional fabrication technique based on anisotropic plasma etching at an oblique angle to the sample surface. As a proof of concept, this angled-etching methodology is used to fabricate free-standing nanoscale components in bulk single-crystal diamond, including nanobeam mechanical resonators, optical waveguides, and photonic crystal and microdisk cavities. Potential applications of the fabricated prototypes range from classical and quantum photonic devices to nanomechanical-based sensors and actuators.