We present a novel scheme for nuclear structure calculations based on realistic nucleon-nucleon potentials. The essential ingredient is the explicit treatment of the dominant interaction-induced correlations by means of the unitary correlation operator method (UCOM). Short-range central and tensor correlations are imprinted into simple, uncorrelated many-body states through a state-independent unitary transformation. Applying the unitary transformation to the realistic Hamiltonian leads to a correlated, low-momentum interaction, which is well suited for all kinds of many-body models, e.g., Hartree-Fock or shell-model. We employ the correlated interaction, supplemented by a phenomenological correction, in the framework of variational calculations with antisymmetrised Gaussian trial states (fermionic molecular dynamics). Ground state properties of nuclei up to mass numbers A[less, approximate]60 are discussed. Binding energies, charge radii, and charge distributions are in good agreement with experimental data. We perform angular momentum projections of the intrinsically deformed variational states (projection after variation) to extract rotational spectra. Finally, we discuss perspectives for variation after projection and multi-configuration calculations.