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In this paper we investigate the error probability for OFDM with carrier frequency offset (CFO) in additive white Gaussian noise (AWGN) and Rayleigh fading channels. The statistical nature of the intercarrier interference (ICI) due to CFO and the validity of the usual Gaussian distributed ICI assumption are studied. In AWGN channels, our simulations indicate that the theoretical symbol error rate (SER) obtained by assuming Gaussian characteristics for the ICI is not accurate. The effect of adjacent channel ICI coefficients must be considered. However in a fading channel provided that the channel correlation effects on the useful OFDM signal and the ICI are considered, the theoretical BER results due to Gaussian ICI approach and simulations closely agree. The theoretical SER for MQAM signaling in fading channels is also derived in closed form.