It is possible to stay friends with an ex, I am living proof of that lol!
My ex and I got together about 5 years ago, and broke up just over 3 years ago. Ok, maybe for a few months after we broke up we were still sleeping together but now we are just friends. She has a new boyfriend who she is very much happy with, I am not jealous in the slightest. In fact, I am happy for her, she is with someone who makes her truly happy. We both thought that I could make her happy but turns out we simply weren't very good as a couple.
Seems strange for some people to believe this but she is still one of my closest friends. We used to talk every single day, and that has changed since she got a new boyfriend, but it's one of those friendships where you won't hear anything from them for a week, but then as soon as you start chatting it's like you carry on where you left off as if nothing happened. There is no awkwardness at all. We both have no intention of taking the friendship any further, and there certainly isn't any sexual attraction coming from anyone.
Her boyfriend isn't completely happy that we're still friends, much less staying in contact, which is understandable. We still meet up every month or so for a proper catch up over dinner. Even though we aren't compatible as a couple, we both have loads in common, we both love the same foods, one of the reasons why we meet up for dinner.
I personally don't know anyone else who is on good terms with an ex partner. It seems that I am the only one out of my circle of friends who is and the same for her. So many people think that something isn't quite right about it, or that something is going on. We're just friends, it's that simple. We know exactly where we stand with eachother and we are fine just being friends.