Several proton-bound cluster ions have been studied by means of coupled cluster calculations with large basis sets. Among these are complexes of a krypton or xenon atom with the cations HCO⁺, HN₂⁺ and HNCH⁺. Various spectroscopic properties have been calculated in all cases. Effects of vibrational anharmonicity are particularly pronounced for the intramolecular stretching vibrations of Kr···HN₂⁺ and Xe···HN₂⁺. The proton stretching vibration of (N₂)H⁺(N₂) is predicted around 800 cm⁻¹, with a large transition dipole moment of 1.15 D. Both (N₂)H⁺(N₂) and (HCN)H⁺(NCH) have linear centrosymmetric equilibrium structures. Those of (OC)H⁺(CO) and (HCC⁻)H⁺(CCH⁻) are asymmetric with barrier heights to the centrosymmetric saddle points of 382 and 2323 cm⁻¹, respectively. The dissociation energy of the anionic complex Cl⁻···HCCH is calculated to be D_o = 3665 cm⁻¹, 650 cm⁻¹ larger than the corresponding value for Br⁻···HCCH. The complex between a fluoride ion and acetylene is more strongly bound and shows strongly anharmonic behaviour, similar to the bihalides FHF⁻ or ClHCl⁻. Strong Fermi resonance interaction is predicted between ν₃ (∽proton stretch) and 2ν₄ (first overtone of intermolecular stretch).