Neural circuit mapping efforts in model organisms are generating multi-terabyte datasets of 10,000s of labelled neurons. Such data demand new computational tools to search and organize neurons. We present a general, sensitive and rapid algorithm, NBLAST, for measuring pairwise neuronal similarity. NBLAST considers both position and local geometry and works by decomposing a query and target neuron into short segments; matched segment pairs are scored using a log-likelihood ratio scoring matrix empirically defined by the statistics of real matches and non-matches. We validated NBLAST by processing a published dataset of 16,129 single Drosophila neurons. NBLAST is sensitive enough to distinguish two images of the same neuron and can be used to distinguish neuronal types without a priori information. Detailed cluster analysis of extensively studied neuronal classes identified new neuronal types and unreported features of topographic organization. NBLAST supports diverse additional query types including matching neurite tracts with transgene expression patterns. We organize all 16,129 neurons into 1,052 clusters of highly related neurons, further organized into superclusters, simplifying exploration and identification of neuronal types including sexually dimorphic and visual interneurons.