Colloidal aggregation is a canonical example of disordered growth far from equilibrium and has been extensively studied for the case of spherical monomers. Many particles encountered in industry and the environment are highly elongated; however, the control of particle shape on aggregation kinetics and structure is not well-known. Here, we explore this control in laboratory experiments that document aqueous diffusion and aggregation of two different elongated colloids: natural asbestos fibers and synthetic glass rods, with similar aspect ratios of about 5:1. We also perform control runs with glass spheres of similar size (similar to 1 mu m). The aggregates assembled from the elongated particles are noncompact, with morphologies and growth rates that differ markedly from the classical aggregation dynamics observed for spherical monomers. The results for asbestos and glass rods are remarkably similar, demonstrating the primacy of shape over material properties suggesting that our findings may be extended to other elongated colloids such as carbon nanotubes/fibers. This study may lead to enhanced prediction of the transport and fate of colloidal contaminants in the environment, which are strongly influenced by the growth and structure of aggregates.