The adsorption of benzene, naphthalene, and anthracene on Cu(111) and its vicinal Cu(221) and Cu(443) surfaces has been studied by means of thermal desorption spectra (TDS) and low energy electron diffraction. For each of the studied acenes (C4n+2H2n+4, n=1,2,3) two distinct binding states were observed in the TDS corresponding to adsorption on terraces and at step edges. The binding energies of both states are found to increase linearly with the number of aromatic rings n. In contrast to the Cu(111) surface where these acenes form disordered adlayers only, ordered films of naphthalene and anthracene with an alignment of the molecular axis along the steps could be prepared on the vicinal surfaces.