Obviously if the ex cheated/lied/was abusive then it's never a good idea.
Relationships break down for all sorts of reasons. I have one ex who I would gladly get back with and so many I wouldn't.
I noticed whilst browsing Facebook on my newsfeed that two girls I know are back with their exs. One posted a photo of the dinner their boyfriend cooked and the other about how many days it is until their holiday.
I have a thought that through every break up you learn why and learn about yourself (what perhaps you were doing wrong in the relationship). If you both learn from your mistakes then it is possible to fall back in love and be happy with each other.
However some people would never go back, and would state "an ex is an ex for a reason".