I think it all depends on the circumstances. If you are the one breaking up it usually takes less time becuase you've been considering it for a while and you've already come to terms with it by the time you say it out loud. If you're the one being broke up with, I think it takes a little longer due to the rejection factor and the ego bash (as well as the usual getting used to not having the other around anymore. Of course those that can't be alone (as Pisces mentions) for very long will jump right out of the frying pan and into the fire never processing their past baggage or learning a lesson from any of it.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion