To date, 204 individual molecular species, comprised of 16 different elements, have been detected in the interstellar and circumstellar medium by astronomical observations. These molecules range in size from two atoms to seventy, and have been detected across the electromagnetic spectrum from cmwavelengths to the ultraviolet. This census presents a summary of the first detection of each molecular species, including the observational facility, wavelength range, transitions, and enabling laboratory spectroscopic work, as well as listing tentative and disputed detections. Tables of molecules detected in interstellar ices, external galaxies, protoplanetary disks, and exoplanetary atmospheres are provided. A number of visual representations of this aggregate data are presented and briefly discussed in context.