It all depends. It's not "yes" or "no". Every case is different.
But...from my experience my, mom remains good friends with her first husband. They still drive each other crazy from time to time, but they will always be friends, they consider each other family. And it's not just because of the kids. In fact, both of their kids (my older brother and sister) are completely grown up, in their mid-twenties, living on their own. But my mom and their dad are still totally friends. It's great, i love them both. They have been friends for as long as i can remember.
My mom and MY dad, however, are not so close. They are civil with each other, but they are very different people. In fact it's hard to imagine how they ever got along in the first place...
It all just depends on the people, how well they deal with problems, how much time has passed since the break-up, how emotionally mature they are, the reasons WHY they broke up in the first place, whether or not there are kids involved, and so on.