The AGN-heated dust distribution (the torus) is increasingly recognized not only as the absorber required in unifying models, but as a tracer for the reservoir that feeds the nuclear Super-Massive Black Hole. Yet, even its most basic structural properties (such as its extent, geometry and elongation) are unknown for all but a few archetypal objects. Since most AGNs are unresolved in the mid-infrared, we utilize the MID-infrared interferometric Instrument (MIDI) at the Very Large Telescope Interferometer (VLTI) that is sensitive to structures as small as a few milli-arcseconds (mas). We present here an extensive amount of new interferometric observations from the MIDI AGN Large Program (2009 - 2011) and add data from the archive to give a complete view of the existing MIDI observations of AGNs. Additionally, we have obtained high-quality mid-infrared spectra from VLT/VISIR. We present correlated and total flux spectra for 23 AGNs and derive flux and size estimates at 12 micron using simple axisymmetric geometrical models. Perhaps the most surprising result is the relatively high level of unresolved flux and its large scatter: The median point source fraction is 70 % for type 1 and 47 % for type 2 AGNs meaning that a large part of the flux is concentrated on scales smaller than about 5 mas (0.1 - 10 pc). Among sources observed with similar spatial resolution, it varies from 20 % - 100 %. For 18 of the sources, two nuclear components can be distinguished in the radial fits. While these models provide good fits to all but the brightest sources, significant elongations are detected in eight sources. The half-light radii of the fainter sources are smaller than expected from the size ~ L^0.5 scaling of the bright sources and show a large scatter, especially when compared to the relatively tight size--luminosity relation in the near-infrared.