We discuss the renormalization of the free energy of a heavy quark anti-quark pair in the singlet, octet and color averaged channels for quenched and full QCD at finite temperature and density. We analyze the temperature and mass dependence of these free energies and discuss their short distance behaviour. From the asymptotic large distance behaviour of the free energies we are able to define the non-perturbative renormalized Polyakov loop which is well behaved in the continuum limit. Using the quenched free energies we calculate the heavy quark potential and entropy. String Breaking is studied in the different color channels in 2-flavour QCD and the effect of a non-zero chemical potential is analyzed using a Taylor expansion of the Polyakov loop correlation function in $\mu_q$.