Graphene has attracted a lot of interest for fundamental studies as well as for potential applications. Till now, micromechanical cleavage (MC) of graphite has been used to produce high-quality graphene sheets on different substrates. Clear understanding of the substrate effect is important for the potential device fabrication of graphene. Here we report the results of the Raman studies of micromechanically cleaved monolayer graphene on standard SiO2 (300 nm)/Si, single crystal quartz, Si, glass, polydimethylsiloxane (PDMS), and NiFe. Our data suggests that the Raman features of monolayer graphene are independent of the substrate used; in other words, the effect of substrate on the atomic/electronic structures of graphene is negligible for graphene made by MC. On the other hand, epitaxial monolayer graphene (EMG) on SiC substrate is also investigated. Significant blueshift of Raman bands is observed, which is attributed to the interaction of the graphene sheet with the substrate, resulting in the change of lattice constant and also the electronic structure.