In this work, a Bayesian framework for OFDM channel estimation is proposed. Using the maximum entropy principle to exploit prior system information at the receiver, we successively derive channel estimates in situations when (i) the channel delay spread and (ii) the channel time correlation statistics are a priori unknown. More generally, this framework allows to derive MMSE channel estimates under any state of knowledge at the receiver. Simulations are provided that confirm the theoretical claims and show the novel results to perform as good or better than classical estimators.