A theory of spin relaxation in graphene including intrinsic, Bychkov-Rashba, and ripple spin-orbit coupling is presented. We find from spin relaxation data by Tombros et al. (Nature, 448 (2007) 571) that intrinsic spin-orbit coupling dominates over other contributions with a coupling constant of 3.7 meV. Although it is 1–3 orders of magnitude larger than those obtained from first principles, we show that comparable values are found for other honeycomb systems, MgB2 and LiC6; the latter is studied herein by electron spin resonance (ESR). We assess the feasibility of bulk electron spin resonance spectroscopy on graphene and identify experimental conditions where such experiments are realizable.