I nofollow (and cloak) all my affiliate links, but I don't have boatloads of them on a single site anywhere.
Personally, I don't think it will hurt you to nofollow them. I am reasonably sure that Google actually has recommended it, but I could be mixing that up with someone else. You don't want them to be mistaken for paid links, and you need to provide a good user experience. And I for one believe strongly that followed linking out (non-aff) is probably considered a Good Thing(tm).
But I don't know how many products/links you're talking about. You might could try adding them a few at a time to see what kind of effect it has.