A dedicated gamma-ray burst (GRB) afterglow observing program was performed between 2007 and 2016 with GROND, a seven-channel optical and near-infrared imager at the 2.2m telescope of the Max-Planck Society at ESO/La Silla, In this first of a series of papers, we describe the GRB observing plan, providing first readings of all so far unpublished GRB afterglow measurements and some observing statistics. In total, we observed 514 GRBs with GROND, including 434 Swift-detected GRBs, representing 81% of the observable Swift sample. For GROND-observations within 30 min of the GRB trigger, the optical/NIR afterglow detection rate is 81% for long- and 57% for short-duration GRBs. We report the discovery of ten new GRB afterglows plus one candidate, along with redshift estimates (partly improved) for four GRBs and new host detections for seven GRBs. We identify the (already known) afterglow of GRB 140209A as the sixth GRB exhibiting a 2175{AA} dust feature. As a side result, we identified two blazars, with one at a redshift of z=3.8 (in the GRB 131209A field).