This paper presents a broadly applicable algorithm and a comprehensive open-source software implementation for automated tracing of neuronal structures in 3-D microscopy images. The core 3-D neuron tracing algorithm is based on three-dimensional (3-D) open-curve active Contour (Snake). It is initiated from a set of automatically detected seed points. Its evolution is driven by a combination of deforming forces based on the Gradient Vector Flow (GVF), stretching forces based on estimation of the fiber orientations, and a set of control rules. In this tracing model, bifurcation points are detected implicitly as points where multiple snakes collide. A boundariness measure is employed to allow local radius estimation. A suite of pre-processing algorithms enable the system to accommodate diverse neuronal image datasets by reducing them to a common image format. The above algorithms form the basis for a comprehensive, scalable, and efficient software system developed for confocal or brightfield images. It provides multiple automated tracing modes. The user can optionally interact with the tracing system using multiple view visualization, and exercise full control to ensure a high quality reconstruction. We illustrate the utility of this tracing system by presenting results from a synthetic dataset, a brightfield dataset and two confocal datasets from the DIADEM challenge.