In this paper, we study the effects of channel estimation error on the bit-error-rate (BER) of orthogonal frequency division multiplexing (OFDM) systems in frequency-selective slowly Rayleigh fading channels. Due to the additive white Gaussian noise (AWGN) and the intercarrier interference (ICI) caused by the residual carrier frequency offset (CFO), the channel estimation based on the training symbols is not perfect. We characterize the performance degradation resulting from imperfect channel state information (CSI) by deriving the BER formulas for BPSK, QPSK, 16-QAM, and 64-QAM modulation schemes. The derived BER formulas contain no numerical integrals and can be evaluated easily and accurately. Simulation results validate the correctness of our theoretical analysis.