Let's stay friends‏

Cliché scene (feel free to reverse roles):

Man: 'I am really sorry, but this isn't working for me'
Woman: 'What do you mean?'
Man: 'You are great, but I can't see this relationship going any further'
Woman: 'Are you dumping me??'
Man: 'No, I mean, yes.. Sorry, didn't want to hurt you.. I do care a lot about you. Please, let's stay friends'
Woman: 'F@#* off'

The question is obvious: can you stay friends with an ex?
Yes, yes, I hear ya, you are in best terms with several of your exes. You are great at maintaining relationships, and regularly in touch for laughs and fun..
Give me a break. This can't be true for all of them, surely.

Whether you can go from mating to mates depends on several factors.
First, the actual relationship. Were you friends before dating? Were you friends in addition to being in love? In both cases, chances are something is recoupable. On the other hand, was the sexual chemistry so tangible you carried an X-rating on your forehead? Were you a bundle of fire together? Was drama on the menu every other day? Then once apart, staying apart may be the best solution.
Second, the break-up. Anything ugly, especially if it involves third parties, is unlikely to bestow a chummy buddy. Broken china and the odd bone are a lot more likely.
Third, children. You have to be civil to each other. To say the least. No choice.
Fourth, and probably most importantly, time. It may look impossible in the aftermath, but years later you may find the most unexpected exes-turned-into-friends by your side. Sharing thoughts, experiences, stories with someone who knows you well, can be very insightful. Someone from a distant place in your past, who understands what you mean and where you coming from.  Someone safe, you can speak to freely, without fear of misinterpretation. Someone you actually like and can make you laugh. Who can quote you back, from forgotten memories, who can predict your choices and cut through the superficial crap. Even if they haven't spoken to you for over a decade.

It is not all that rosy, though. There can be perils to be aware of. Specifically, the flame must be truly and utterly dead. For both parties. No hang-ups and no secret hopes.

And, of course, the good old dilemma: can a man and a woman be just friends? But that's another story.