This study reports Raman and infrared spectra of hybrid organic-inorganic MAPbX3 perovskites (MA = CH3NH3, X = Cl, Br, I) and their mixed-halide derivatives. Raman spectra were recorded at three laser wavelengths (514, 785, and 1064 nm) under on- and off-resonance conditions, as well as at room temperature and 100 K. The use of different excitation wavelengths allowed the unambiguous acquisition of "true" Raman spectra from the perovskites, without degradation or photoinduced structural changes. Low-frequency PbX vibrational modes were thoroughly identified by comparison of Raman and far-IR results. Red Raman frequency shifts for almost all MA vibrations from 200 to 3200 cm-1, and particularly intense for the torsional mode, were observed toward heavy halide derivatives, indicative of strengthening the interaction between halides and the organic cation inside the inorganic cage. Different MA-X bonding schemes are evidenced by torsional mode pairs emerging in the orthorhombic phase. MAPbBr3 was further characterized by variable temperature Raman measurements (100-295 K). Broadening of the MA rocking mode slightly above the tetragonal I to II phase transition is connected with disorder of the MA cation. Our results advance the understanding of perovksite materials properties (ferroelectric domain formation, anomalous hysteresis) and their use as efficient light absorbers in solar cells.