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So let's say you are widgets-store.com.
You might rank #15 for "widgets."
However, if you have a really good affiliate, they might be able to boost your ranking to #8 for widgets, but your site URL might come up as their affiliate url, widgets-store.com/index.html?aid=666 or whatever.
Some people would call that a help. ;-)
Actually, if your affiliates engage in hardcore spam tactics, you could be penalized for it. That is possible.
If you simply add a few aff links to an already established website with content and such, you're probably safe.
However, if you build a website around aff links with no substantial content... expect a really low ranking.
Google especially doesn't like affiliate websites that offer little content. In general however I'd say that your ok as long as there is content there for visitors to see.