The imaging Compton telescope COMPTEL aboard NASA's Compton Gamma-Ray Observatory has opened the MeV gamma-ray band as a new window to astronomy. COMPTEL provided the first complete all-sky survey in the energy range 0.75 to 30 MeV. The catalogue, presented here, is largely restricted to published results. It contains firm as well as marginal detections of continuum and line emitting sources and presents upper limits for various types of objects. The numbers of the most significant detections are 32 for steady sources and 31 for gamma-ray bursters. Among the continuum sources, detected so far, are spin-down pulsars, stellar black-hole candidates, supernova remnants, interstellar clouds, nuclei of active galaxies, gamma-ray bursters, and the Sun during solar flares. Line detections have been made in the light of the 1.809 MeV 26Al line, the 1.157 MeV 44Ti line, the 847 and 1238 keV 56Co lines, and the neutron capture line at 2.223 MeV. For the identification of galactic sources, a modelling of the diffuse galactic emission is essential. Such a modelling at this time does not yet exist at the required degree of accuracy. Therefore, a second COMPTEL source catalogue will be produced after a detailed and accurate modelling of the diffuse interstellar emission has become possible.