The MAC access delay in a saturated IEEE 802.11 DCF wireless LAN is analyzed. We develop a unified analytical model and obtain explicit expressions for the first two moments as well as the generating function. We show via comparison with simulation that our model accurately predicts the mean, standard deviation, and distribution of the access delay for a wide range of operating conditions. In addition, we show that the obtained generating function is much more accurate than others that have appeared in the literature. Using our model, we prove that the binary exponential backoff mechanism induces a heavy-tailed delay distribution for the case of unlimited retransmissions. We show using numerical examples that the distribution has a truncated power-law tail when a retransmission limit exists. This finding suggests that DCF is prone to long delays and not suited to carrying delay-sensitive applications.