I would have to say that each situation is different and yes it is possible to be friends with your ex. I am and I always will be. Every relationship begins and ends differently, not every situation is black and white. Yes it has been a process of self discovery and learning to live and get on with life with out a partner. We all get hurt in some way or another we learn to accept our own personal situation and overcome what ended the relationship in the beginning. I personally have never been the type to hold a grudge and choose to believe that certain situations happen for a reason.
There are guidelines you need to consider to whether you should be friends with your ex. They are
You have to truly want to be friends with your ex - it is important to understand that the romantic relationship is over and that you are strictly friends with no romantic inclinations or benefits.
You need to forgive each other regardless on how the relationship finished - it is impossible to be friends if you are hostile towards each other, it just will not work and will continue to be toxic. You need to move on to forgive and forget to be friends.
You need to support each other in future relationships - You and your ex will inevitably find a new love interest and you both have to be ok with this. Jealousy will complicate things and you must genuinely want the best for each other and respect the decision made with whom ever they choose to move on with.
Accept that friendship is not for everyone - You cannot force the friendship between to people to continue if their is anger or hostility between you both.