We discuss the renormalization of the free energy of a heavy quarkanti-quark pair in the singlet, octet and color averaged channelsfor quenched and full QCD at finite temperature and density.We analyze the temperature and mass dependence of these freeenergies and discuss their short distance behaviour. From the asymptotic large distance behaviourof the free energies we are able todefine the non-perturbative renormalized Polyakov loop which iswell behaved in the continuum limit.Using the quenched free energies we calculate the heavy quarkpotential and entropy.String Breaking is studied in the differentcolor channels in 2-flavour QCD and the effect of a non-zero chemicalpotential is analyzed using a Taylor expansion of the Polyakov loopcorrelation function in $\mu_q$.