Both IE8 and FF have a browser privacy mode. I think it's "In private browsing" in Internet Explorer, and "Start Private Browsing" in Firefox. I guess that most other browsers will have this option in the next version if they don't have it today.
I'd say it's extremely difficult to be able to assess the current impact on affiliates as they just appear as normal visitors to the merchant. But I think the saving grace at the moment is that most customers don't use it.
WR