It isn't always the easiest of situations.
I think it really depends on how that relationship was and how said couple ended things. I'm a very forgiving person and I want to believe the best in people.
So with me, I've tried remaining friends with both my ex's. I've had about 4 real serious boyfriends, but the last two I had were the most meaningful ones to me. With Chris, it was really easy. I met him when I was 18 and were friends before, and even though the way it ended was a sleazy thing for him to do, I've always been able to be real good friends with him. It's easy because he didn't always treat me badly. And after it ended I found myself getting over him and forgiving him rather quickly. Of course, at the same time I found myself rebound very quickly with Rick.
But trying to be friends with Rick? Oh fuck. That has always been hard for me to do. LOL we had been so off and on for years. And our relationship was so unhealthy and hard. When he really broke up with me in Sept of O8 it was difficult. In that case, I had to cut off all communications with him... he's the hardest person I have ever had to get over. But then he found himself wanting to be friends and yada yada. It was an endless of should they or shouldn't be friends. Cause regardless, we were always drawn back to each other. LOL and now we are friends again, but only cuz the girl he was seeing dumped him. It's hard for me to be friends with him. I'm always going to feel for him, and that isn't good. But I choose when I'm friends with Rick.
Sorry I went into detail, but I'm just sharing my experiences. Like I said, it depends on how the relationship ended and how intense you guys were. It always isn't easy, and it can be done.