In this paper, we study the effects of channel estimation error on the bit error rate (BER) of orthogonal frequency division multiplexing systems in multipath Rayleigh fading channels. Due to the additive white Gaussian noise and the intercarrier interference caused by the residual carrier frequency offset, the channel estimation based on the training symbols is not perfect. We characterize the performance degradation resulting from imperfect channel state information by deriving the BER formulas for BPSK, QPSK, and 16-QAM modulation schemes. Simulation results validate the accuracy of our derived formulas.