We consider charge transport through a nanoscopic object such as single molecules or coupled quantum dots, that is weakly coupled to metallic electrodes. We explicitly account for the electronic interactions and the resulting many-body states of the molecule/quantum dots, and allow for relaxation of the excited states. The current-voltage characteristics as well as the current noise are calculated within first-order perturbation expansion in the coupling strengths. For the case of a semi-quantitative model of benzene we predict negative-differential-conductance accompanied with super-poissonian noise. For a series coupled quantum dots, we analyze the shot noise in the various regimes of transport depending on the inter-dot coupling and participating many-body states.