I looked into this a few days ago....
There was much guff about Pandas and Farmers to wade through, but best intell I could find was that:
'Paid Text Links' - bad, use nofollow.
Affiliate Links - not so clear.
Big G clearly has a dim view of 'I'll give you 50 quid to post some boiler-plate crap with a link to my site'. Probably rightly so. So if you use nofollow, you can pocket the 50 without G penalty. Probably. Conspiracy theorists may point out that G may well follow the link anyway - just to see why you nofollowed it!
For Affiliate Links, G seems quite understanding that we may make money from our sites. So these links per se are not bad. It was not at all clear to me from my searching around whether these should be nofollowed or not.
Whether Affiliate Links drain juice, or whether the linked-to content is supporting your site theme, or whatever other metric may be in play,... is a whole big discussion, and is probably called SEO
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BTW I did spot a post somewhere about something that had never occured to me. A suggestion that footer links to your Privacy Policy, T&Cs and whatever other non-theme-specific pages you may have on your site, should be nofollowed. Makes sense. Some general legalese waffle is probably diluting your site-wide keyword / theme specificity.
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Mike