Hi,
yes, you can run SSRS on Standard edition.
Please review comparing features by edition
http://msdn.microsoft.com/en-us/library/cc645993(v=sql.105).aspx/css
Features Supported by the Editions of SQL Server 2008 R2
and scroll down to the Reporting section. I think even the web edition supports it.
This article also allow you to navigate to other versions, use the dropdown right below the article title.
Yelena
Regards,Yelena Varsha