This paper analyzes the maximum steady throughput and optimum media access control (MAC) of a random access system over channels with retransmission gain. The channel is defined by the packet detection probability of each user as a function of the numbers of packet transmissions and collisions. The maximum steady throughput and stability region for two-user channels are obtained in closed form. The conditions that the maximum throughput is reached with control-free MAC are obtained. The well-known results of the orthogonal and the ALOHA channels are shown to be special instances of our results. The throughputs of multiuser symmetric channels and the general multiuser asymmetric channel are further obtained. A practical random access CDMA channel exploiting retransmission diversity is analyzed based on the model. Numerical result confirms with the analytical results. It is conclude that retransmission gain can significantly increase throughput and expand stability region.