Well, I think right after the break-up there should be a time where the two individuals can heal and move on without having a lot of contact with each other. Then, after a while, if both people agree, I believe there should be a certain level of friendship, depending on the reason for the break-up.
A few months ago I broke up with my boyfriend and we both agreed to still be friends. I have tried to keep my end of the bargain, but he has totally treated me like an outcast, so.........I guess it would depend on the individual if they wanted to be friends or not. I could, but he didn't want to, so we just leave each other alone.