Graphene, a one-atomic-layer-thick planar sheet of sp(2)-bonded carbon configured in a two-dimensional hexagonal lattice, has attracted considerable research interest with regard to sensing-related applications owing to its extraordinary electronic, optical, chemical, and mechanical properties. Graphene plasmonics may be excited in the mid-infrared-to-terahertz regions with high spatial confinement, low loss, and excellent tunability. Meanwhile, graphene can be utilized to tune the plasmonic properties of conventional metallic nanostructures in the visible and near-infrared regions, allowing it to act as a versatile component in various plasmonic applications. This article reviews the recent progress in graphene-based hybrid films used for plasmonic sensing and detection. We particularly emphasize on the unique roles and advantages of graphene in surface-enhanced Raman scattering (SERS) for bare graphene or graphene-metal hybrid films, and plasmonic refractive index (RI) sensing for graphene-metal or graphene-insulator hybrids, among other plasmonic sensing applications. The preparation of graphene-based hybrid films, their functionalization and signal detection techniques are also reviewed. Finally, the perspectives and current challenges in the use of graphene-based hybrid films for plasmonic sensing are outlined.