Measurements of b-hadron lifetimes are reported using p p collision data, corresponding to an integrated luminosity of 1.0 fb(-1), collected by the LHCb detector at a centre-of-mass energy of 7 TeV. Using the exclusive decays B+ -> J/psi K+, B-0 -> J/psi K* (892)(0), B-0 -> J/K-s(0), Lambda(0)(b) -> J/psi Lambda and B-s(0) -> J/psi phi the average decay times in these modes are measured to be tau(B+) -> J/psi K+ = 1.637 +/- 0.004 +/- 0.003 p s, tau(B0) -> J/psi K*(0) = 1.524 +/- 0.006 +/- 0.004 p s, tau(0)(B) -> J/psi K-s(0) = 1.499 +/- 0.013 +/- 0.005 ps, tau Lambda(0)(b) -> J/psi Lambda = 1.415 +/- 0.027 +/- 0.006 ps, tau(0)(Bs) -> J/psi phi = 1.480 +/- 0.011 +/- 0.005 ps, where the first uncertainty is statistical and the second is systematic. These represent the most precise lifetime measurements in these decay modes. In addition, ratios of these lifetimes, and the ratio of the decay-width difference, Delta Gamma(d), to the average width, Gamma(d), in the B-0 system, Delta Gamma(d)/Gamma(d) = -0.044 +/- 0.025 +/- 0.011, are reported. All quantities are found to be consistent with Standard Model expectations.