I haven't really had any success with trying to be friends after a break-up; although, for this purpose I'm definitely making an assumption that we're talking about serious relationships. Don't get me wrong, I've really tried... but it usually ends up burning in flames.
At the end of the day, I think it's hard to be friends with someone who you were in a serious relationship. For me, there's a reason why I was attracted to that person, and there was a reason why I dated them. There's also a reason (or reasons) why we're no longer a couple. Once certain boundaries in a relationship are crossed, it's hard to re-establish them, whether you read that as "sex" or "arguments" or merely "passion", it doesn't really matter.
And, when the other party starts dating again... there's always the "what if's..." that come along with watching him/her find a life without you playing a major part in it.
Yes, I'm totally friendly with a number of my exes... but we're not friends, we're in some weird other-world category of "people I care about but don't really know if I want to know about it... but I hope they're doing well!" I am in the circle of friends with a number of exes, and we live in the same town. Yes, we run into each other, yes, we're okay with that. We even smile and introduce each others parties and might sit down for a drink before parting ways. It's rarely awkward; however, it's definitely not a "wow, I'm going to call him and tell him all about that <insert funny story here>." relationship.
I don't know if that makes any sense, and yes, I know people who have managed to do it (although I know for a fact that the two people who I am speaking of have some relationship holdups and have yet to settle back into ANY normal relationship because a lot of their needs are being filled by their 'ex'; so the only thing they look for elsewhere is whatever is missing in their current weird-friendship-ex-relationship); however, I don't think I'm either at the maturity or at the point in my life where being friends with an ex is a good idea. And yes, I'm a slow learner. I still crash and burn with one of my exes on a regular basis.