Inverse kinematics is fundamental for computational motion planning. It is used to derive an appropriate state in a robot's configuration space, given a target position in task space. In this work, we investigate the performance of fully connected and residual artificial neural networks as well as recurrent, learning-based, and deep spiking neural networks for conventional and geometrically constrained inverse kinematics. We show that while highly parameterized data-driven neural networks with tens to hundreds of thousands of parameters exhibit sub-ms inference time and sub-mm accuracy, learning-based spiking architectures can provide reasonably good results with merely a few thousand neurons. Moreover, we show that spiking neural networks can perform well in geometrically constrained task space, even when configured to an energy-conserved spiking rate, demonstrating their robustness. Neural networks were evaluated on NVIDIA's Xavier and Intel's neuromorphic Loihi chip.