Surface-enhanced Raman spectroscopy (SERS) is a potent analytical tool, particularly for molecular identification and structural analysis. Conventional metallic SERS substrates, however, suffer from low reproducibility and compatibility with biological molecules. Recently, metal-free SERS substrates based on chemical enhancement have emerged as a promising alternative with carbon-based materials offering excellent reproducibility and compatibility. Nevertheless, our understanding of carbon materials in SERS remains limited, which hinders their rational design. Here we systematically explore multidimensional carbon materials, including zero-dimensional fullerenes (C60), one-dimensional carbon nanotubes, two-dimensional graphene, and their B-, N-, and O-doped derivatives, for SERS applications. Using density functional theory, we elucidate the nonresonant polarizability-enhanced and resonant charge-transfer-based chemical enhancement mechanisms of these materials by evaluating their static/dynamic polarizability and electron excitation properties. This work provides a critical reference for the future design of carbon-based SERS substrates, opening a new avenue in this field.