Do you mean to say that the forums rewrite the URLs the users paste in such a way, or that the links on the forum itself (vs. the links in posts) are affiliate marketing?
Not at all of them do it, but for the motoring section a large number rewrite the eBay ones because the value of a click-through on a high ticket item like a car is enormous (relative to the affiliate fee for a book or CD).
There's only two ways to pull it off: 1) You audience is kinda dumb and doesn't know (wouldn't work on reddit), or 2) You just come clean and say you're going to do it as it is one of the most viable ways in which to make the site fund itself and to produce a profit (which would work on reddit because it's not intrusive and wouldn't change what people are doing already).
In the latter case you need to make sure no-one games it. There is enough click fraud detection to make this the next problem... once you've tapped into a gushing well of money you really need to make sure that the actions of your own community don't turn it off. Which effectively means trying to make sure that no-one is gaming your system (with best intentions to help you) with fake click-throughs.
But even there, a work-around is to provide your own proxy to the click traffic and to run something to detect abnormal traffic... if it looks to be outside of a set of parameters, strip out the affiliate info and redirect as normal. This minimises the risk of losing the revenue stream once it's been acquired.
The more I hear about this, the more I think that reddit could pull it off. If they came clean, I really doubt there would be any discontent at all. The only problem might be that most of the links are imgur links nowadays, but they could make lots of money even from the occasional amazon review link.
If they stuck to pay-per-action affiliate links, like Amazon's, for example, they wouldn't even need to police it for gaming (I don't think Amazon would mind people buying things to help reddit out).
