It has recently become possible to attach metallic contacts to individual organic molecules, opening up a new field of study for investigating transport of individual molecules. With electromigration, we make nanogaps on an aluminum gate electrode between which single molecules are trapped. Three-terminal measurements on samples with the same molecule (OPV-5, Co4L4 grid molecule, Mn-12, single-metal atom complexes) share common features showing Coulomb blockade and Kondo physics at low temperature. Of crucial importance is the observation of molecule-specific properties as deduced for example from the interaction between electronic transport and vibrational modes or spin states in the molecule. Transport measurements through an individual thiol end-capped oligophenylenevinylene molecule with five benzene rings (OPV-5) show that the spin states, the charging energies, and the electronic spectrum are completely renormalized by the presence of the gold electrodes. In case of the doubly charged molecule the data indicate delocalized orbitals with an anti-ferromagnetic ground state and an exchange of 1.7 meV.