Molecules of manganese hydrides MnH2, MnH2-, and MnH3 were studied using large basis sets up to spdfg quality and the coupled cluster technique for the treatment of electron correlation. Both MnH2 and MnH2- have linear equilibrium structures in their high spin ground electronic state, the MnH2- molecule having a rather flat bending potential. The MnH3 molecule is Y-shaped with valence angle alpha(H-Mn-H) = 44.6degrees in the 5132 ground electronic state due to the strong Jahn-Teller distortion of the trigonal planar structure. The harmonic vibrational frequencies, IR intensities, and the relative energies of excited states were calculated. Fundamental vibrational wavenumbers and electron affinity were also found for MnH2. The results are compared with available spectroscopic data.