A continuum model for the effective spin-orbit interaction in graphene is derived from a tight-binding model which includes the pi and sigma bands. We analyze the combined effects of the intra-atomic spin-orbit coupling, curvature, and applied electric field, using perturbation theory. We recover the effective spin-orbit Hamiltonian derived recently from group theoretical arguments by Kane and Mele. We find, for flat graphene, that the intrinsic spin-orbit coupling Deltaint[proportional]Delta2 and the Rashba coupling due to a perpendicular electric field [script E], Delta_{[script E]}[proportional]Delta, where Delta is the intra-atomic spin-orbit coupling constant for carbon. Moreover we show that local curvature of the graphene sheet induces an extra spin-orbit coupling term Deltacurv[proportional]Delta. For the values of [script E] and curvature profile reported in actual samples of graphene, we find that Deltaint<Delta_{[script E]}<~Deltacurv. The effect of spin-orbit coupling on derived materials of graphenelike fullerenes, nanotubes, and nanotube caps, is also studied. For fullerenes, only Deltaint is important. Both for nanotubes and nanotube caps Deltacurv is in the order of a few Kelvins. We reproduce the known appearance of a gap and spin-splitting in the energy spectrum of nanotubes due to the spin-orbit coupling. For nanotube caps, spin-orbit coupling causes spin-splitting of the localized states at the cap, which could allow spin-dependent field-effect emission.