Here we examine the effects of folding and scrolling on the Raman spectra of mechanically exfoliated single- and bilayer graphene prepared on SiO(2) substrates. We find that incommensurate folding in bilayer graphene results in a shift of the second-order G' band frequency, similar to that observed in folded single-layer graphene due to fold-induced changes in the phonon/electronic energy dispersion. Importantly, we show that the contrasting Raman shifts reported for the G' band frequency in folded graphene can be rationalized by taking into account the relative strength of fold-induced electron/phonon renormalization. More interestingly, we find that curvature in scrolled graphene lifts the degeneracy of the G band and results in a splitting of the G band and the appearance of low-frequency radial breathing-like (RBLM) modes. This study highlights a variety of Raman signatures for fold-induced and curvature-induced graphene and sets the stage for further theoretical and experimental studies of these novel structures.