The adsorption of uracil on Au(111) and Au(100) from sulfuric acid solution has been studied by in-situ scanning tunneling microscopy (STM). Depending on the potential applied to the Au(hkl) electrode, uracil forms highly ordered two-dimensional physisorbed as well as chemisorbed adlayers, which were imaged with molecular resolution in-situ. "Steady-state" and time-dependent experiments were performed in order to follow structural changes of the respective substrate surfaces in the presence of these organic layers. The physisorbed films on Au(111)-(p x root 3), Au(100)-(hex), and Au(100)-(1 x 1) are rather similar. They display characteristic properties of a hydrogen-bonded network of planar oriented uracil molecules. The influence of the substrate surface geometry for these systems was primarily reflected in the dimensions of the respective coincidence cells. At sufficiently positive electrode potentials, uracil deprotonates and forms highly ordered chemisorbed, perpendicularly oriented surface coordination complexes. The organic molecule occupies (root 3 x root 3)R30 degrees-positions of the Au(111)-(1 x 1) lattice. An additional experimentally observed contrast pattern between adjacent rows of molecules is explained by the formation of interdigitated rows of molecules rotated +45 degrees and -45 degrees with respect to the [110] direction of the substrate surface. The chemisorbed uracil film on Au(100)-(1 x 1) is of oblique symmetry and consists of interdigitated regular arrays of stacks, each containing four molecules.