Biological systems are organized into well-ordered structures and can evolve new patterns when perturbed. To identify principles underlying biological order, we turned to C. elegans for its simple anatomy and powerful genetics. We developed a method to quantify the arrangement of three dendrites in the main sensory nerve bundle, and found that they exhibit a stereotyped arrangement throughout larval growth. Dendrite order does not require prominent features including sensory cilia and glial junctions. In contrast, loss of the cell adhesion molecule (CAM) CDH-4/Fat-like cadherin causes dendrites to be ordered randomly, despite remaining bundled. Loss of the CAMs PTP-3/LAR or SAX-7/L1CAM causes dendrites to adopt an altered order, which becomes increasingly random as animals grow. Misexpression of SAX-7 leads to subtle but reproducible changes in dendrite order. Our results suggest that combinations of CAMs allow dendrites to self-organize into a stereotyped arrangement and can produce altered patterns when perturbed.