When you save a Query or Report you can define it as a Web report which does not require to logon.
When being opened in the Report Web Service this Report will not require the user to provide logon credentials.

This option allows to open a Web report without logging in.
To edit an objects property right click it and select Properties.


Edit the "Allow anonymous access" settings.
Related
Report Web Service Functionality
Install - Move - the Report Webservice on a Server