To better understand the functional roles of hippocampal forward and reverse replays, we trained rats in a spatial sequence memory task and examined how these replays are modulated by reward and navigation history. We found that reward enhances both forward and reverse replays during the awake state, but in different ways. Reward enhances the rate of reverse replays, but it increases the fidelity of forward replays for recently traveled as well as other alternative trajectories heading toward a rewarding location. This suggests roles for forward and reverse replays in reinforcing representations for all potential rewarding trajectories. We also found more faithful reactivation of upcoming than already rewarded trajectories in forward replays. This suggests a role for forward replays in preferentially reinforcing representations for high-value trajectories. We propose that hippocampal forward and reverse replays might contribute to constructing a map of potential navigation trajectories and their associated values (a "value map") via distinct mechanisms.