Techniques are described for providing customizable sign-on functionality, such as via an access manager system that provides single sign-on functionality and other functionality to other services for use with those services' users. The access manager system may maintain various sign-on and other account information for various users, and provide single sign-on functionality for those users using that maintained information on behalf of multiple unrelated services with which those users interact. The access manager may allow a variety of types of customizations to single sign-on functionality and/or other functionality available from the access manager, such as on a per-service basis via configuration by an operator of the service, such as co-branding customizations, customizations of information to be gathered from users, customizations of authority that may be delegated to other services to act on behalf of users, etc., and with the customizations that are available being determined specifically for that service.