This paper is concerned with the challenging and timely problem of data detection for coded orthogonal frequency-division multiplexing (OFDM) systems in the presence of frequency-selective and very rapidly time varying channels. New low-complexity maximum a posteriori probability (MAP) data detection algorithms are proposed based on sequential detection with optimal ordering (SDOO) and sequential detection with successive cancellation (SDSC). The received signal vector is optimally decomposed into reduced dimensional subobservations by exploiting the banded structure of the frequency-domain channel matrix whose bandwidth is a parameter to be adjusted according to the speed of the mobile terminal. The data symbols are then detected by the proposed algorithms in a computationally efficient way by means of the Markov chain Monte Carlo (MCMC) technique with Gibbs sampling. The impact of the imperfect channel state information (CSI) on the bit error rate (BER) performance of these algorithms is investigated analytically and by computer simulations. A detailed computational complexity investigation and simulation results indicate that, particularly, the algorithm based on SDSC has significant performance and complexity advantages and is very robust against channel estimation errors compared with existing suboptimal detection and equalization algorithms proposed earlier in the literature.