2015 and they do not accept Discover cards.
I can think of several good reasons to use American Express, despite it being somewhat less widely accepted. But Discover doesn't seem to have any obvious value over a MasterCard or Visa.
[1]https://www.discover.com/credit-cards/help-center/account/in...
[1] http://www.amazon.co.uk/gp/help/customer/display.html?nodeId... or http://www.amazon.de/gp/help/customer/display.html?nodeId=50...