Depending on the situation, IMO ex's can be friends. However, my definition of friends with an ex means we are kind to each other. We shared a history and don't have to "act like we hate each other". I never understood that and don't want to have an ex that I hate. It will take years to get to this level if the relationship was serious and long term. If it was a bf/gf you knew you would not spend your life with, it would not take long at all, maybe. If you broke up because you two were not compatible enough for a long term relationship then I don't see an issue with remaining friends. It depends to the maturity of the couple. Not many people can deal with occasionally talking or hanging out with an ex.
You get major points if you can be kind to an ex. Being friends with an ex can be weird for many. You have to be over the relationship and not have expectations.
If the relationship was bad or abusive then you would not want them to be your friends anyway.
If you can't handle me at my worst, then you sure as hell don't deserve me at my best. ~ Marilyn Monroe