Origami can turn a sheet of paper into complex three-dimensional shapes, and similar folding techniques can produce structures and mechanisms. To demonstrate the application of these techniques to the fabrication of machines, we developed a crawling robot that folds itself. The robot starts as a flat sheet with embedded electronics, and transforms autonomously into a functional machine. To accomplish this, we developed shape-memory composites that fold themselves along embedded hinges. We used these composites to recreate fundamental folded patterns, derived from computational origami, that can be extrapolated to a wide range of geometries and mechanisms. This origami-inspired robot can fold itself in 4 minutes and walk away without human intervention, demonstrating the potential both for complex self-folding machines and autonomous, self-controlled assembly.