Precise measurements of the lifetimes of the $B^0$, $B_s^0$, $\Lambda_b^0$, and $B_c^+$ hadrons using the decay channels $B^0 \to J/\psi K^{*}(892)^0$, $B^0 \to J/\psi K_s^{0}$, $B_s^0 \to J/\psi \pi^+ \pi^-$, $B_s^0 \to J/\psi \phi(1020)$, $\Lambda_b^0 \to J/\psi \Lambda^0$, and $B_c^+ \to J/\psi \pi^+$ were performed. The data sample, corresponding to an integrated luminosity of 19.7 fb$^{-1}$, was collected by the CMS detector at the LHC in proton-proton collisions at $\sqrt{s}=8$ $\textrm{TeV}$. The $B^0$ lifetime is measured to be $453.0 \pm 1.6\textrm{(stat)} \pm 1.5\textrm{(syst)} $ $\mu\textrm{m}$ in $J/\psi K^{*}(892)^0$ and $457.8 \pm 2.7\textrm{(stat)} \pm 2.7\textrm{(syst)} $ $\mu\textrm{m}$ in $J/\psi K_s^{0}$. The effective lifetime of the $B_s^0$ meson is measured in two decay modes, with contributions from different amounts of the heavy and light eigenstates. This results in two different measured lifetimes: $c\tau_{B_s^0 \to J/\psi \pi^+ \pi^-} = 502.7 \pm 10.2\textrm{(stat)} \pm 3.2\textrm{(syst)} $ $\mu\textrm{m}$ and $c\tau_{B_s^0 \to J/\psi \phi(1020)} = 443.9 \pm 2.0\textrm{(stat)} \pm1.2\textrm{(syst)}$ $\mu\textrm{m}$. The $\Lambda_b^0$ lifetime is found to be $442.9 \pm 8.2\textrm{(stat)} \pm 2.7\textrm{(syst)}$ $\mu\textrm{m}$. The precision from each of these channels is as good as or better than previous measurements. The $B_c^+$ lifetime, measured with respect to the $B^+$ to reduce the systematic uncertainty, is $162.3 \pm 8.2\textrm{(stat)} \pm 4.7\textrm{(syst)} \pm 0.1\,(\tau_{B^+})$ $\mu\textrm{m}$. All results are in agreement with current world-average values.