  Generic quantum systems --as much as their classical counterparts-- pass
arbitrarily close to their initial state after sufficiently long time. Here we
provide an essentially exact computation of such recurrence times for generic
non-integrable quantum models. The result is a universal function which depends
on just two parameters, an energy scale and the effective dimension of the
system. As a by-product we prove that the density of orthogonalization times is
zero if at least nine levels are populated and connections with the quantum
speed limit are discussed. We also extend our results to integrable, quasi-free
fermions. For generic systems the recurrence time is generally doubly
exponential in the system volume whereas for the integrable case the dependence
is only exponential. The recurrence time can be decreased by several orders of
magnitude by performing a small quench close to a quantum critical point. This
setup may lead to the experimental observation of such \emph{fast} recurrences.
