I don't see the point in trying to be friends with someone after they hurt you (or you hurt them) emotionally, which is usually what happens...sour feelings with the other person after you break up. I don't think there's many relationships out there that end where both people are perfectly happy moving on from each other and rainbows, cupids, and butterflies shoot out everywhere and there's this perfectly happy ending with the two people going their separate ways.
There would have to be a reason to want to continue having them in your life after everything is said and done. One is you (or the other person) wants to continue being in each others lives for whatever reason...to always keep you on the back burner as a back up, or who knows. Another thing might be "ohhh yeah we are friends now, so I don't necessarily need to commit to you per say, but I still wouldn't mind getting with you every now and then (friends with benefits)." I've never been down for that and I never will be.
There are certain kinds of people who may think that way, but most of the people I know wouldn't do that. I have plenty of friends who do not talk to exes because relationships ended badly, but some catch up with exes to see how they are and/or because they are now good friends.
One of my best friends is an ex. We dated in 2008 for 3 months and I ended the relationship because he wasn't right for me. He's an incredible, kind, sensitive person and he asked if we could stay friends. We met a week or so after we had broken up, which was a little strange, but after that, everything was fine. He and I both feel that our relationship led to a really good friendship. He and I go to one another for advice in the same way two long-term friends would - we have been friends for 5 years, so that's only natural! There are absolutely no additional feelings there at all, emotional or physical.
I used to talk to all but one of my exes; I didn't talk to one because we had dated for a month and we had nothing in common. I recently cut ties to four of my exes for different reasons. However, it had nothing to do with the fact we used to date.
For example, I cut ties with my first boyfriend because he was a terrible friend. When we broke up in 2007, he was incredibly nasty to me. He told my friends that I was a liar and tried to manipulate me into telling my parents that I had broken up with him for someone else, which wasn't true. Nevertheless, I always wanted to make sure that he was okay and happy. Based on what I knew, he had an incredibly difficult life. I continued to talk to him to support him and to offer advice. However, he grew more negative over the years. About 3 months ago, was annoyed with me because I don't post about my life on Facebook anymore and because I hadn't spoken to him much. I have been incredibly busy completing a PGCE this year, which I explained to him. He then told me that I shouldn't be in a relationship because that was probably making things more difficult. I tried to justify myself at first, but later on told him kindly not to offend my relationship again. He proceeded to delete me and I decided that I should stop accepting his negativity. I can't actually do anything for him - he has to find a way to be happy - so I haven't spoken to him since.
I am at a point in my life where I want to focus on positive relationships. If friends go through anything rough, I will be there for them, but this 'friend' had been mildly abusive for years. I don't have time for something like that, ex or not.