Rayg (from Feedster) asks, "If search engines are so willing to pimp their space to sponsored links, why ... [not add] an affiliate ID in the [search result] links?" Ray goes on to argue that the move would largely go unnoticed and wouldn't damage credibility.
Jeremy Zawodny (from Yahoo) disagrees, saying that this would blur the lines between sponsored and non-sponsored results too badly. Even if the relevance rank is unbiased by the affiliates revenue, the perception that some links are paid would damage the credibility of the search engine.
I have wondered if Yahoo and Google have considered adding affiliate links, not to their search engine, but to their metashopping searches (Yahoo Shopping and Froogle).
But Jeremy's point that probably applies to shopping search as well. It would look like a conflict of interest and potentially damage credibility, even if the affiliates revenue did not influence their relevance rank.