Controllable assembly of ordered nanoscale structural units in geometrically well-defined configurations is essential for building integrated nanoscale systems. Here, we describe a powerful method to simultaneously grow aligned carbon nanotube bundles in multiple, predetermined orientations on planar substrates to build one- to three-dimensional architectures. We effect multidirectional nanotube growth by gas-phase delivery of a xylene-ferrocene mixture on to lithographically machined silica surface templates. The preference of nanotubes to grow normal to, and selectively on, silica surfaces forces the nanotubes to inherit the topography of the substrate templates, enabling premeditated selection of both nucleation sites and growth direction. By using silica templates of different shapes, we can build a wide variety of organized nanotube structures of differing complexity and shapes, density, dimensions, and orientation, for example, mutually orthogonal arrays of pillars and platelets, films with hierarchical pores, and free-standing membranes. This fabrication route is scalable to large areas and compatible with silicon microfabrication technology and opens up attractive possibilities for constructing nanotube architectures for applications such as electronic switching, electromechanical actuation, and fluidic separation.