On this site, I've seen it used 3 ways:
'Backpedal', 'backpaddle', and 'back peddle.'
My pointless correction of the day is to clarify that when using this idiom, 'backpedal' is the correct term, and the only one cited in the dictionary as the act of retracting a statement. I don't know if it is just a spelling issue or if it is confusion about the words themselves, but peddle, pedal, and paddle are different words with different meanings.
The term 'backpedaling' is in reference to pedaling backward on a bike, hence the use of the words 'backing out of' a stance in its definition. Back-paddling is actually a word, but it references the backward motion of rowing a boat and isn't recognized in the same fashion. Peddling is trying to sell something, so contextually, there really is no proper way to even use the term 'backpeddling'.
So there it is. Feel free to add your own, correct any misinformation, or fix any grammar I may have missed or may not have used at all in this post.