I have never personally broken up with someone, i've usually been the one who has been dumped, or it was a mutual break up. My boyfriend broke up with me and i was devastated. He still adored me, I think he was going through a stage in his life where he felt he wasn't ready for commitment (I was planning to move cities to be with him). I believe that freaked him out. We still kept in touch over the proceding weeks of the break up, because as you can imagine, being the dumped, I wanted to be in his life either way. Eventually we hook up 5 weeks later after I had made that move anyway, and he regretted splitting with me and knew I was the love of his life after realising what it was like during that time apart. However, it's made me, understandably, nervous and mistrustful in case he dumps me again. It's hard to make that decision to go back to someone who dumped you, but I loved - love him.
It depends on the circumstances. My boyfriend never cheated, as far as i am aware, and I think it is natural to go through stages in a relationship and feel claustrophobic and always wondering whether the grass is greener. I know he probably did sleep around during that break, but we were single people, and that's what i have to accept. If one of the parties cheated, that is an entirely different matter, and i wouldnt get back with someone who cheated on me. If they were abusive, again i wouldnt get back with them. It depends whether you can both overcome the problems what were responsible for the break up in the first place.
What is your situation?