I've just read this question (now deleted). What is the policy on putting affiliate tags into Amazon links on Stack Overflow? What about other affiliate links?
I think that flagging any affiliate link as spam is overly harsh. Posts should be edited to remove the affiliate indication in compliance with the policy. Put a link to this thread in the edit summary and leave a comment on one post so that the user is notified through their inbox.
Harsher measures should only be taken if a user keeps including affiliate links after having been pointed to the policy. If a user remains deaf to comments or rolls the affiliate link back in, flag one of their posts for moderator attention and explain the situation.
Depends on what is going on. If you are answering a question concerning books or products and you are giving examples of really good books, I would more or less look past it (because if they are the one giving me the product for the first time and I like it, I wouldn't mind giving them some kickback for the review).
If they are asking a question or something and it is more blatantly spam trying to sell products without any real value behind it (or if that review or link is not a good idea on that particular question/answer) then I will be like ChrisF and flag it as spam.
I would say that if the affiliate links are not affecting the answer in any way, to leave them in. If a person gives a great answer that happens to include a few affiliate links, so long as those links are completely relevant, then there is no harm in it. Especially if Stack Exchange doesn't have a link of their own to the question.
My example would be this answer. The same quality of answer is there with or without the affiliate links, but the affiliate links give the poster of the answer a chance to make a small amount of money that would otherwise be lost (Actually, the various service providers would essentially make that money, giving them completely free advertisement).
However, if a person is showing an obvious bias, or self-promoting products, then they should be removed completely and quickly.