When you plan to integrate SSRS 2008 R2 with SharePoint 2010, it is a common scenario that DBA install SSRS and Sharepoint administrator does the configuration for integrate mode. Often times DBA just let SSRS run under a built-in account such as LocalSystem or NetworkService, and let a poor sharepoint guy do the rest of work. In order to run SSRS in an integrated mode, the first thing to do is to change its service account to a domain account. Then here comes the problem: in the sharepoint central admin, when you try to configure "Reporting Service Integration", you get an error saying failure to connect to RS!
Don't doubt about your typing skills or about your memory of your password or anything else (of course you need to check network communication between your sharepoint server and RS server, such as firewall etc). The problem is: if you ever run SSRS under a built-in account, the RS is automatically configured to run in a Kerberos authentication, and it stays that way even after the service account is changed into a domain account. Kerberos works by default if the service is running under a built-in account, but it breaks when service is running under a domain account unless you register the SPN.
As now you know why it breaks, the solution is simply, either manually change the authentication type to "RSWindowsNTLM" in reportserver.config. or register SPN to the domain service account. see this post for details.