Please double check to make sure that the username and password you are using is correct. You can verify this by logging into the CRM Organization directly.
Please check to make sure that the Discovery Service or Organization Service URL has been entered properly. For more information about your Discovery URL please see Microsoft's documentation here.
If MFA is enabled for your organization, ensure that you have read through the documentation here.
Some organizations have a specific TLS protocol configured for their organization. You can change this setting in the connection dialog under the 'Advanced' tab.
If the time difference between your local machine and the CRM server is greater than 5 minutes then CRM may not allow you to connect to it.
Please verify that the CRM user account has enough privileges to connect via the SDK. Generally speaking a user with either the 'System Administrator' or 'System Customizer' role should be used. In the case of plugins, if you are trying to register your plugin outside of the sandbox then you will need to be a CRM Deployment Administrator.
Please verify that all the appropriate firewall ports have been opened so that you can reach the different CRM endpoints.
XrmToolkit uses the CRM SDK behind the scenes to connect with the organization. The requirement of having Windows Identity Foundation installed is due to the SDK and the way it connects to the organization. Windows Identity Foundation is a free download from Microsoft here: Windows Identity Foundation Download
If the memory usage (RAM) of the server exceeds 95% then IIS shuts down and/or does not allow the CRM webservices to be started. You would see event logs on the server indicating this.