What Traygon said.. it doesn't really help at all unless the site you're affiliating with really is related to your subject.. for example, I am affiliated with a political news forum on my political debate forum.. this actually helps, where as me affiliating with a gaming forum for example wouldn't do anything beneficial.
We don't affiliate with forums in terms of we put their button on here and they put ours on theirs. Many people do out of good will put our button on their sites and collectively they bring in alot of traffic although that is mainly down to the high number of people who has added the button. If only 4 sites had added our button we would not get many hits if any per day.
I agree with Irviding. You have to affiliate with something related to the topic of your forum to have people interested when they see your affiliate button on another user's site.
With awesome styles I've set up two 'affiliate deals' (far more than just swapping a button, but we do that too) and traffic they bring in is worth it for us and vice versa for them.
So yes, they can work, but you need to pick relevent sites with lots of traffic/users.
Affiliating with any old forum is useless I'm afraid!