During development and metastasis, cells migrate large distances through complex environments. Migration is often guided by chemotaxis, but simple chemoattractant gradients between a source and sink cannot direct cells over such ranges. We describe how self-generated gradients, created by cells locally degrading attractant, allow single cells to navigate long, tortuous paths and make accurate choices between live channels and dead ends. This allows cells to solve complex mazes efficiently. Cells' accuracy at finding live channels was determined by attractant diffusivity, cell speed, and path complexity. Manipulating these parameters directed cells in mathematically predictable ways; specific combinations can even actively misdirect them. We propose that the length and complexity of many long-range migratory processes, including inflammation and germ cell migration, means that self-generated gradients are needed for successful navigation.