I think that it happens a lot, but... it's hard to say whether it's a good idea or not. I've slept with an ex after breaking up before. I didn't really have plans on getting back together with her, though. I would guess that the majority (>50%) of times this happens it doesn't end up with a re-kindled, happy, long-lasting relationship, though. That being said, is that really the most important thing?
Normal? Yes. Good idea? Subjective.