Graphite has been intensively studied, yet its electron spins dynamics remains an unresolved problem even 70 years after the first experiments. The central quantities, the longitudinal (T-1) and transverse (T-2) relaxation times were postulated to be equal, mirroring standard metals, but T-1 has never been measured for graphite. Here, based on a detailed band structure calculation including spin-orbit coupling, we predict an unexpected behavior of the relaxation times. We find, based on saturation ESR measurements, that T-1 is markedly different from T-2. Spins injected with perpendicular polarization with respect to the graphene plane have an extraordinarily long lifetime of 100 ns at room temperature. This is ten times more than in the best graphene samples. The spin diffusion length across graphite planes is thus expected to be ultralong, on the scale of similar to 70 mu m, suggesting that thin films of graphite - or multilayer AB graphene stacks - can be excellent platforms for spintronics applications compatible with 2D van der Waals technologies. Finally, we provide a qualitative account of the observed spin relaxation based on the anisotropic spin admixture of the Bloch states in graphite obtained from density functional theory calculations.