Before you start, ensure that your server is configured to allow Single Sign-On (SSO). If you have a Remote Desktop Session Host, the Always Prompt for Password setting should not be set for the connection in Properties>Log on Settings and also on the General tab, the Security Layer should be set to Negotiate or SSL.
Also, SSO needs to be enabled on your local / domain policy. Check the value of Allow Delegating Default Credentials here in your GPO:
Computer Configuration\Administrative Templates\System\Credentials Delegation
Also ensure that your server (TERMSRV/) is added to the server list, if required. You may use wild card characters to add multiple server names
When you run the Remote Desktop Connection, you should tick the box for Allow me to save credentials.

You will then be prompted to enter your credentials. When you do so, ensure you tick the box for Remember my credentials. Your credentials should then be saved, and next time you log in it will be passed through.

Here is a link with some basic step by step instructions: http://itowns.blogspot.co.uk/2011/06/enabling-remote-desktop-connection.html
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If you're asked for credentials by Remote Desktop, then you haven't successfully set SSO - even if you "remember" your credentials. That's kind of the whole point of SSO. The above screenshots are junk; they SHOULD look like this: http://i.imgur.com/JQbVaFN.png
– James Johnston – 2016-05-24T02:44:11.567