The organic cations in hybrid organic-inorganic perovskites rotate rapidly inside the cuboctahedral cavities formed by the inorganic lattice, influencing optoelectronic properties. Here, we provide a complete quantitative picture of cation dynamics for formamidinium-based perovskites and mixed-cation compositions, which are the most widely used and promising absorber layers for perovskite solar cells today. We use 2H and 14N quadrupolar solid-state NMR relaxometry under magic-angle spinning to determine the activation energy (Ea) and correlation time (τc) at room temperature for rotation about each principal axis of a series of organic cations. Specifically, we investigate methylammonium (MA+), formamidinium (FA+), and guanidinium (GUA+) cations in current state-of-the-art single- and multi-cation perovskite compositions. We find that MA+, FA+, and GUA+ all have at least one component of rotation that occurs on the picosecond timescale at room temperature, with MA+ and GUA+ also exhibiting faster and slower components, respectively. The cation dynamics depend on the symmetry of the inorganic lattice but are found to be insensitive to the degree of cation substitution. In particular, the FA+ rotation is invariant across all compositions studied here, when sufficiently above the phase transition temperature. We further identify an unusual relaxation mechanism for the 2H of MA+ in mechanosynthesized FAxMA1-xPbI3, which was found to result from physical diffusion to paramagnetic defects. This precise picture of cation dynamics will enable better understanding of the relationship between the organic cations and the optoelectronic properties of perovskites, guiding the design principles for more efficient perovskite solar cells in the future.