In light of the intense recent interest in the methylammonium lead halides, CH3NH3PbX3 (X = Cl, Br, and I) as sensitizers for photovoltaic cells, the dynamics of the A methylammonium (MA) cation in these perovskite salts has been reinvestigated as a function of temperature via H-2, N-14 and Pb-207 NMR spectroscopy. In the cubic phase of all three salts, the MA cation undergoes pseudoisotropic tumbling (picosecond time scale). For example, the correlation time, tau(2), for the C-N axis of the iodide salt is 0.85 +/- 0.30 ps at 330 K. The dynamics of the MA cation are essentially continuous across the cubic H tetragonal phase transition; however, H-2 and N-14 NMR line shapes indicate that subtle ordering of the MA cation occurs in the tetragonal phase. The temperature dependence of the cation ordering is rationalized using a six-site model, with two equivalent sites along the c-axis and four equivalent sites either perpendicular or approximately perpendicular to this axis. As the cubic 4-tetragonal phase transition temperature is approached, the six sites are nearly equally populated. Below the tetragonal H orthorhombic phase transition, H-2 NMR line shapes indicate that the C-N axis is essentially frozen.