All three are used, but I think that 'ragged' might be used more often to describe a cough rather than breathing in general. That is not to say that its use with breathing is incorrect.
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AlpheccaStarsragged mountains = No. Use "rugged mountains" for the general term. There are mountains with the name "Ragged Mountains ," but that is a proper name.I'm sure I was thinking "rugged" when I first replied to this post, but now, come to think of it, if I look at a two-dimensional picture of a mountain range, the term "ragged" seems oddly appropriate