I am using reporting services 2010 and get the following prompt when trying to access the reports:
The previous select solution could not work for someone (It didn't for me), so I will show you how can you bypass it. SSRS used internet explorer to run those requests in the background (even if you use other browsers), so the solution will be adding a different type of Authentication to IE. Go to:
Open Internet Explore -> Internet Options -> Custom -> user authentication select "Automatic logon with current user name and password"