Hmm. None of my former lovers are close friends, but I am still close friends with some of the women I dated (and got to sexy times short of becoming lovers).
In my experience, Esper is maybe half-right. It depends on the nature of the breakup (usually easier if you haven't gone all the way), and also on other factors like mutual friends, how often you see each other later on, residual feelings you both have, and how they get on with your current partner.
With my wife it was friendship first. We hadn't been close friends more than ~3 mos. before we became lovers, nonetheless she's still my closest friend.