FeedsAnywhere now supports password-less syncing with Google Reader using the OAuth protocol. I've been incrementally transitioning from the old ClientLogin method that required a user to provide the username and password for their Google Account to the newer OAuth method.
The benefit is better security through not having to give out a password while still maintaining control of who has access to your account. FeedsAnywhere only asks for access to Google Reader and that's all we can touch. You can also revoke access at any time through your Google Account settings.
Please let us know if you encounter any issues.