  The annihilation rate of dark matter particles plays a crucial role in dark
matter studies, for it determines their relic density and their indirect
detection signal. In this paper, we show that this annihilation rate can
receive large additional contributions from three-body final states consisting
of a real and a virtual massive particle, such as WW* (Wf \bar f') and t \bar
t* (tW\bar b). We consider two specific examples, from the singlet model and
the MSSM, and find that, due to the new three-body final state contributions,
the prediction for the relic density may decrease by more than a factor two,
whereas the present dark matter annihilation rate gets enhanced by up to two
orders of magnitude. Some of the implications of these results are briefly
discussed.
