  We show that polynomial decay of correlations is prevalent for a class of
nonuniformly hyperbolic flows. These flows are the continuous time analogue of
a class of nonuniformly hyperbolic diffeomorphisms for which Young proved
polynomial decay of correlations. Roughly speaking, in situations where the
decay rate $O(1/n^{\beta})$ has previously been proved for diffeomorphisms, we
establish the decay rate $O(1/t^\beta)$ for typical flows. Applications include
certain classes of semidispersing billiards, as well as dispersing billiards
with vanishing curvature. In addition, we obtain results for suspension flows
with unbounded roof functions. This includes the planar periodic Lorentz flow
with infinite horizon.
