Question: Usually if you connect to a Remote Desktop Session Host running on a Windows Server 2008 R2 you will be prompted for your credentials and if they are valid you will be logged in to your session directly.

On one of our servers everyone who logs on with RDP sees the usual Windows Logon Screen (green/blue background with username/password) after already entering them in the Remote Desktop Client. So, users are not directly logged in, but have to enter their credentials twice. It is only the case for this server. The server also is a Remote Desktop Connection Broker. 

Is this behavior caused by a wrong setting or do you know how to get rid of it?

Answer: 
I had a wrong setting enabled: Session Host Configuration -> Select the connection -> properties -> Credentials tab.

Here you can choose where to always ask for credentials or take the credentials provided by the client.
We have that enabled on our of our machines through a GPO. Take a look at this setting: Windows Components/Remote Desktop Services/Remote Desktop Session Host/Security under Computer Configuration/Administrative Templates and look for this setting: Always prompt for password upon connection Enabled