In the case of Amazon, perhaps the Associates Web Service APIs could allow the creation of tool allowing user-defined sorting functions. I've never used these APIs, but I found some details on them that lead me to think it would be possible. See http://aws.amazon.com/associates/#details

That said, asking honestly, are you entirely convinced of the mass appeal of user-defined (or user-selected) sorting algorithms? I find that the current algorithm usually gives fairly sane results.

(Edit: rewrote last sentence for clarity)