Friends are supposed to trust each other, I can't really be friends with a chronic cheater because I know I can't trust them. I can be civil with them.
SO like COGuy pointed out it partly depends on the reason for divorce - if it was just due to mutual dissatisfaction with living together and there was no abuse, no cheating or no other kinds of betrayal of trust I could see former spouses remaining friends.
As for me, I am an amicable co-parent to my ex. When she first was telling me she wanted out of the marriage so she could find someone better she was already spouting about us acting like best friends and not lovers, and how much better it would be if we just were best friends - I looked at her like "what kind of drug are you on?".
We are not really enemies, nor friends in the least, but we are allies in raising our child together. That's all it is.