The successful isolation of high quality graphene, which is essentially a single layer of graphite, has opened up a new field of materials science and low-dimensional physics. Graphene oxide based materials attract vast attention and have been applied into various fields of sensors, photovoltaics, field effect transistors and memory devices. Nonvolatile memory devices can store information/data even when power is off, can be programmed/erased/read many times, and allow long-term data storage. Nonvolatile memory devices based on graphene oxide can be a promising approach towards a low-cost memory technology. As dynamic random access memory (DRAM) and flash memory have technological and physical limitations towards low power, the small size non-volatile resistive random access memory (RRAM) devices have gain much attention because of their high speed, long retention time, low power consumption and simple geometry. A typical RRAM device with metal-insulator-metal (MIM) structure undergoes the phenomenon of resistance change when stimulated by electrical signal. The resistive switching effect has been explored till now in number of materials including transition metal oxides, perovskite oxides, organic materials and carbon based materials. Among carbon based materials, Graphene oxide (GO) is a material of great interest for its special quality, and its electrical properties can be modified by altering the attached chemical groups. In contrast to metallic nature of Graphene, the Graphene oxide (GO) is good insulating/semiconducting material, which can be readily obtained by oxidizing graphite with strong oxidants. Presence of hydroxyl, epoxy and other functional groups enhance the electrical resistivity of GO, resulting GO as an insulator and suitable for RRAM device applications. In first approach, we fabricated RRAM devices composed of pristine graphene oxide (Pt/GO/ITO) MIM structures on ITO coated glass substrate with Platinum (Pt) as the top electrode and observed the forming free bipolar resistive switching characteristics. The repeatable and reliable bipolar resistive switching was observed with good on/off ratio over number of cycles. Comparable bipolar resistive switching was also observed at elevated temperature of 500 K with on/off ratio of 102 with good endurance and retention characteristics. This study indicates the stability and non-volatility of devices at room and high temperatures. In second approach, we have investigated the RRAM characteristics in graphene oxide complexes. These complexes were fabricated by making heterostructure of reduced graphene with polymer having structure (Pt/PVDF/GR/PVDF/ITO) on ITO coated glass substrate with Platinum (Pt) as the top electrode, by incorporating ZnO nanorods in graphene oxide (Al/GOZNs/ITOPET) structure on flexible ITOPET substrate and also by embedding gold nanoparticles in graphene oxide (Al/GOAu/ITO) structure on ITO coated glass substrate and these devices were found to have multi-level switching for high density data storage memories, tunable power switching for flexible/bendable memories and forming free enhanced switching characteristics with low operating voltages and high on/off ratio respectively. GO and its complexes studied in this thesis were found to be one of the potential candidate for practical RRAM memory device applications.