Hydrazine-reduced graphite oxide and graphene oxide were synthesized to compare their performances as anode materials in lithium-ion batteries and sodium-ion batteries. Reduced graphite oxide inherits the layer structure of graphite, with an average spacing between neighboring layers (d-spacing) of 0.374 nm; this exceeds the d-spacing of graphite (0.335 nm). The larger d-spacing provides wider channels for transporting lithium ions and sodium ions in the material. We showed that reduced graphite oxide as an anode in lithium-ion batteries can reach a specific capacity of 917 mA h g-1, which is about three times of 372 mA h g-1, the value expected for the LiC6 structures on the electrode. This increase is consistent with the wider d-spacing, which enhances lithium intercalation and de-intercalation on the electrodes. The electrochemical performance of the lithium-ion batteries and sodium-ion batteries with reduced graphite oxide anodes show a noticeable improvement compared to those with reduced graphene oxide anodes. This improvement indicates that reduced graphite oxide, with larger interlayer spacing, has fewer defects and is thus more stable. In summary, we found that reduced graphite oxide may be a more favorable form of graphene for the fabrication of electrodes for lithium-ion and sodium-ion batteries and other energy storage devices.