Stoichiometric RMnO3 perovskites have been prepared in the widest range of R3+ ionic sizes, from PrMnO3 to ErMnO3. Soft-chemistry procedures have been employed; inert-atmosphere annealings were required to synthesize the materials with more basic R cations (R = Pr, Nd), in order to minimize the unwanted presence of Mn4+. On the contrary, annealings in O2 flow were necessary to stabilize the perovskite phases for the last terms of the series, HoMnO3, ErMnO3, and YMnO3, thus avoiding or minimizing the formation of competitive hexagonal phases with the same stoichiometry. The samples have been investigated at room temperature by high-resolution neutron powder diffraction to follow the evolution of the crystal structures along the series. The results are compared with reported data for LaMnO3. The distortion of the orthorhombic perovskite (space group Pbnm), characterized by the tilting angle of the MnO6 octahedra, progressively increases from Pr to Er due to simple steric factors. Additionally, all of the perovskites show a distortion of the MnO6 octahedra due to the orbital ordering characteristic of the Jahn-Teller effect of Mn3+ cations. The degree of orbital ordering slightly increases from La to Tb and then remains almost unchanged for the last terms of the series. The stability of the crystal structure is also discussed in light of bond-valence arguments.