The Algebraic Reconstruction Technique (ART) reconstructs a 2D or 3D object from its projections. It has, in certain scenarios, many advantages over the more popular Filtered Backprojection approaches and has also recently been shown to perform well for 3D cone-beam reconstruction. However, so far, ART's slow speed has prohibited its routine use in clinical applications. Currently, a software implementation requires several hours for a 3D reconstruction, even on modest reconstruction grid sizes. Although one solution to combat these problems would be the time-consuming design of expensive custom accelerator boards, we would rather like to resort to existing and widely available hardware for our purposes. In this sense, we find that ART's main operations, i.e., volume projections and image backprojections, can be performed very rapidly on standard 2D texture mapping hardware, resident in many graphics workstations and PC graphics boards. In this paper, we discuss the use of this hardware in two volume decomposition modes: voxel and slice. Although we find that the speedups obtained in the voxel mode are respectable, the speedups obtained in the slice-mode are tremendous. Here, a quality cone-beam reconstruction on a 1283 grid can be obtained in less than 2 minutes, which corresponds to a speedup of over 70. Since our rapid ART reconstruction algorithm can be run on the same workstations that are typically used for the viewing of clinical datasets, it is immediately available for routine parallel- and cone-beam CT.