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In this paper, we derive closed form bit error rate (BER) expressions for orthogonal frequency division multiplexing (OFDM) systems with residual carrier frequency offset (CFO). Most of the published work treats CFO as a nonrandom parameter. But in our study we consider it as a random parameter. The BER performance of binary phase shift keying (BPSK) OFDM system is analyzed in the cases of additive white Gaussian noise (AWGN), frequency-flat and frequency-selective Rayleigh fading channels.We further discuss how these expressions can be related to systems with practical estimators. The simulation results are provided to verify the accuracy of these error rate expressions.